Calculus: Early Transcendental Functions (MindTap Course List)
Calculus: Early Transcendental Functions (MindTap Course List)
6th Edition
ISBN: 9781285774770
Author: Ron Larson, Bruce H. Edwards
Publisher: Cengage Learning
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Optimization
Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the se…
Integration
Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integratio…
Application of Integration
In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.
Volume
In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects th…
Area
Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.
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Chapter 5.6, Problem 40E

Circumference The elliptic integral 8 3 ∫ 0 π / 2 1 − 2 3 sin 2 θ d θ gives the circumference of an ellipse. Use Simpson’s Rule with n = 8 to approximate the circumference.

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Chapter 5 Solutions

Calculus: Early Transcendental Functions (MindTap Course List)

Ch. 5.1 - Integration and Differentiation In Exercises 5 and...Ch. 5.1 - Integration and Differentiation In exercises 5 and...Ch. 5.1 - Solving a Differential Equation In Exercises 7-10,...Ch. 5.1 - Prob. 4ECh. 5.1 - Solving a Differential Equation In Exercises 7-10,...Ch. 5.1 - Prob. 6ECh. 5.1 - Rewriting Before Integrating In Exercises 11-14,...Ch. 5.1 - Complete the following table to find the...Ch. 5.1 - Rewriting before Integrating in Exercises 11-14,...Ch. 5.1 - Rewriting Before Integrating In Exercises 11-14,...
Ch. 5.1 - Prob. 11ECh. 5.1 - Prob. 12ECh. 5.1 - Finding an Indefinite Integral In Exercises 15-36,...Ch. 5.1 - (i) Find the indefinite integral (x+12x)dx (ii)...Ch. 5.1 - Finding an Indefinite Integral In Exercises 15-36,...Ch. 5.1 - Finding an Indefinite Integral In Exercises 15-36,...Ch. 5.1 - Finding an Indefinite Integral In Exercises 15-36,...Ch. 5.1 - Finding an Indefinite Integral In Exercises 15-36,...Ch. 5.1 - Finding an Indefinite Integral In Exercises 15-36,...Ch. 5.1 - Prob. 15ECh. 5.1 - Prob. 16ECh. 5.1 - Prob. 18ECh. 5.1 - Finding an Indefinite Integral In Exercises 15-36,...Ch. 5.1 - Prob. 24ECh. 5.1 - Finding an Indefinite Integral In Exercises 15-36,...Ch. 5.1 - Finding an Indefinite Integral In Exercises 15-36,...Ch. 5.1 - Finding an Indefinite Integral In Exercises 15-36,...Ch. 5.1 - Finding an Indefinite Integral In Exercises 15-36,...Ch. 5.1 - Finding an Indefinite Integral In Exercises 15-36,...Ch. 5.1 - Finding an Indefinite Integral In Exercises 15-36,...Ch. 5.1 - Finding an Indefinite Integral In Exercises 15-36,...Ch. 5.1 - Finding an Indefinite Integral In Exercises 15-36,...Ch. 5.1 - Prob. 33ECh. 5.1 - Sketching a Graph In Exercises 33 and 34, the...Ch. 5.1 - Finding a Particular Solution In Exercises 37-44,...Ch. 5.1 - Prob. 36ECh. 5.1 - Finding a Particular Solution In Exercises 37-44,...Ch. 5.1 - Prob. 38ECh. 5.1 - Finding a Particular Solution In Exercises 37-44,...Ch. 5.1 - Finding a Particular Solution In Exercises 37-44,...Ch. 5.1 - Finding a Particular Solution In Exercises 37-44,...Ch. 5.1 - Finding a Particular Solution In Exercises 37-44,...Ch. 5.1 - Prob. 43ECh. 5.1 - Prob. 44ECh. 5.1 - Prob. 45ECh. 5.1 - Prob. 46ECh. 5.1 - Prob. 47ECh. 5.1 - Prob. 48ECh. 5.1 - Prob. 50ECh. 5.1 - Prob. 49ECh. 5.1 - Prob. 51ECh. 5.1 - Prob. 52ECh. 5.1 - Finding a Derivative In Exercises 43-66. find the...Ch. 5.1 - Finding a Derivative In Exercises 43-66. find the...Ch. 5.1 - Finding a Derivative In Exercises 43-66. find the...Ch. 5.1 - Finding a Derivative In Exercises 43-66. find the...Ch. 5.1 - Prob. 57ECh. 5.1 - Prob. 58ECh. 5.1 - Prob. 59ECh. 5.1 - Finding a Derivative In Exercises 43-66. find the...Ch. 5.1 - Finding a Derivative In Exercises 43-66. find the...Ch. 5.1 - Prob. 62ECh. 5.1 - Prob. 63ECh. 5.1 - Prob. 64ECh. 5.1 - Prob. 65ECh. 5.1 - Finding an Equation of a Tangent Line In exercises...Ch. 5.1 - Prob. 67ECh. 5.1 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.1 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.1 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.1 - Prob. 71ECh. 5.1 - Prob. 72ECh. 5.1 - Prob. 73ECh. 5.1 - Prob. 74ECh. 5.1 - Prob. 75ECh. 5.1 - Prob. 76ECh. 5.2 - Prob. 69ECh. 5.2 - Prob. 1ECh. 5.2 - Prob. 2ECh. 5.2 - Finding a Sum In Exercises 5-10, find the sum by...Ch. 5.2 - Prob. 4ECh. 5.2 - Prob. 5ECh. 5.2 - Prob. 6ECh. 5.2 - Prob. 7ECh. 5.2 - Prob. 8ECh. 5.2 - Prob. 9ECh. 5.2 - Prob. 10ECh. 5.2 - Prob. 11ECh. 5.2 - Prob. 12ECh. 5.2 - Prob. 13ECh. 5.2 - Evaluating a Sum In Exercises 17-24, use the...Ch. 5.2 - Evaluating a Sum In Exercises 17-24, use the...Ch. 5.2 - Evaluating a Sum In Exercises 17-24, use the...Ch. 5.2 - Evaluating a Sum In Exercises 17-24, use the...Ch. 5.2 - Evaluating a Sum In Exercises 17-24, use the...Ch. 5.2 - Prob. 19ECh. 5.2 - Evaluating a Sum In Exercises 17-24, use the...Ch. 5.2 - Evaluating a Sum In Exercises 25-28, use the...Ch. 5.2 - Evaluating a Sum In Exercises 25-28, use the...Ch. 5.2 - Prob. 23ECh. 5.2 - Evaluating a Sum In Exercises 25-28, use the...Ch. 5.2 - Approximating the Area of a Plane Region In...Ch. 5.2 - Approximating the Area of a Plane Region In...Ch. 5.2 - Prob. 27ECh. 5.2 - Prob. 28ECh. 5.2 - Prob. 29ECh. 5.2 - Prob. 30ECh. 5.2 - Prob. 31ECh. 5.2 - Using Upper and Lower Sums In Exercises 35 and 36,...Ch. 5.2 - Prob. 33ECh. 5.2 - Prob. 34ECh. 5.2 - Prob. 35ECh. 5.2 - Prob. 36ECh. 5.2 - Prob. 37ECh. 5.2 - Finding a Limit In Exercises 3742. find a formula...Ch. 5.2 - Prob. 39ECh. 5.2 - Prob. 40ECh. 5.2 - Prob. 41ECh. 5.2 - Prob. 42ECh. 5.2 - Prob. 43ECh. 5.2 - Prob. 44ECh. 5.2 - Prob. 45ECh. 5.2 - Prob. 46ECh. 5.2 - Prob. 47ECh. 5.2 - Prob. 48ECh. 5.2 - Prob. 49ECh. 5.2 - Prob. 50ECh. 5.2 - Prob. 51ECh. 5.2 - Prob. 52ECh. 5.2 - Prob. 53ECh. 5.2 - Prob. 54ECh. 5.2 - Prob. 55ECh. 5.2 - Prob. 56ECh. 5.2 - Prob. 57ECh. 5.2 - Prob. 58ECh. 5.2 - Prob. 59ECh. 5.2 - Prob. 60ECh. 5.2 - Prob. 61ECh. 5.2 - Approximating Area with the Midpoint Rule In...Ch. 5.2 - Prob. 63ECh. 5.2 - Prob. 64ECh. 5.2 - Prob. 65ECh. 5.2 - Prob. 66ECh. 5.2 - Prob. 67ECh. 5.2 - Prob. 68ECh. 5.2 - Prob. 70ECh. 5.2 - Graphical Reasoning Consider the region bounded by...Ch. 5.2 - Prob. 72ECh. 5.2 - Prob. 73ECh. 5.2 - Prob. 74ECh. 5.2 - Prob. 75ECh. 5.2 - Prob. 76ECh. 5.2 - Prob. 77ECh. 5.2 - Prob. 78ECh. 5.2 - Prob. 79ECh. 5.3 - Evaluating a Limit In Exercises 3 and 4, use...Ch. 5.3 - Evaluating a Limit In Exercises 3 and 4, use...Ch. 5.3 - Evaluating a Definite Integral as a Limit In...Ch. 5.3 - Evaluating a Definite Integral as a Limit In...Ch. 5.3 - Evaluating a Definite Integral as a Limit In...Ch. 5.3 - Evaluating a Definite Integral as a Limit In...Ch. 5.3 - Evaluating a Definite Integral as a Limit In...Ch. 5.3 - Evaluating a Definite Integral as a Limit In...Ch. 5.3 - Writing a Limit as a Definite Integral In...Ch. 5.3 - Prob. 10ECh. 5.3 - Writing a Limit as a Definite Integral In...Ch. 5.3 - Prob. 12ECh. 5.3 - Writing a Limit as a Definite Integral In...Ch. 5.3 - Writing a Limit as a Definite Integral In...Ch. 5.3 - Writing a Definite Integral In Exercises 15-26,...Ch. 5.3 - Writing a Definite Integral In Exercises 15-26,...Ch. 5.3 - Writing a Definite Integral In Exercises 15-26,...Ch. 5.3 - Writing a Definite Integral In Exercises 15-26,...Ch. 5.3 - Writing a Definite Integral In Exercises 15-26,...Ch. 5.3 - Writing a Definite Integral In Exercises 15-26,...Ch. 5.3 - Writing a Definite Integral In Exercises 15-26,...Ch. 5.3 - Writing a Definite Integral In Exercises 15-26,...Ch. 5.3 - Writing a Definite Integral In Exercises 15-26,...Ch. 5.3 - Writing a Definite Integral In Exercises 15-26,...Ch. 5.3 - Writing a Definite Integral In Exercises 15-26,...Ch. 5.3 - Writing a Definite Integral In Exercises 15-26,...Ch. 5.3 - Evaluating a Definite Integral Using a Geometric...Ch. 5.3 - Prob. 28ECh. 5.3 - Evaluating a Definite Integral Using a Geometric...Ch. 5.3 - Evaluating a Definite Integral Using a Geometric...Ch. 5.3 - Evaluating a Definite Integral Using a Geometric...Ch. 5.3 - Prob. 32ECh. 5.3 - Evaluating a Definite Integral Using a Geometric...Ch. 5.3 - Prob. 34ECh. 5.3 - Evaluating a Definite Integral Using a Geometric...Ch. 5.3 - Prob. 36ECh. 5.3 - Prob. 37ECh. 5.3 - Prob. 38ECh. 5.3 - Prob. 39ECh. 5.3 - Prob. 40ECh. 5.3 - Prob. 41ECh. 5.3 - Prob. 42ECh. 5.3 - Prob. 43ECh. 5.3 - Prob. 44ECh. 5.3 - Prob. 45ECh. 5.3 - Prob. 46ECh. 5.3 - Prob. 47ECh. 5.3 - Using Properties of Definite Integrals Given...Ch. 5.3 - Estimating a Definite Integral Use the table of...Ch. 5.3 - Prob. 50ECh. 5.3 - Think About It The graph of f consists of line...Ch. 5.3 - Think About It The graph of f consists of line...Ch. 5.3 - Think About It Consider a function f that is...Ch. 5.3 - Prob. 54ECh. 5.3 - Prob. 55ECh. 5.3 - Think About It A function f is defined below. Use...Ch. 5.3 - Prob. 57ECh. 5.3 - Prob. 58ECh. 5.3 - Prob. 59ECh. 5.3 - Prob. 60ECh. 5.3 - Prob. 61ECh. 5.3 - Prob. 62ECh. 5.3 - Prob. 63ECh. 5.3 - Prob. 64ECh. 5.3 - Prob. 65ECh. 5.3 - Prob. 66ECh. 5.3 - Prob. 67ECh. 5.3 - Prob. 68ECh. 5.3 - Prob. 69ECh. 5.3 - Prob. 70ECh. 5.3 - Prob. 71ECh. 5.3 - Prob. 72ECh. 5.3 - Prob. 73ECh. 5.3 - Prob. 74ECh. 5.3 - Prob. 75ECh. 5.3 - Prob. 76ECh. 5.3 - Prob. 77ECh. 5.3 - Prob. 78ECh. 5.3 - Prob. 79ECh. 5.3 - Prob. 80ECh. 5.3 - Prob. 81ECh. 5.3 - Prob. 82ECh. 5.4 - Graphical Reasoning In Exercises 5-8, use a...Ch. 5.4 - Graphical Reasoning In Exercises 5-8, use a...Ch. 5.4 - Graphical Reasoning In Exercises 5-8, use a...Ch. 5.4 - Graphical Reasoning In Exercises 5-8, use a...Ch. 5.4 - Prob. 5ECh. 5.4 - Evaluating a Definite Integral In Exercises 538,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 9-34,...Ch. 5.4 - Prob. 8ECh. 5.4 - Prob. 9ECh. 5.4 - Evaluating a Definite Integral In Exercises 9-34,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 9-34,...Ch. 5.4 - Prob. 12ECh. 5.4 - Evaluating a Definite Integral In Exercises 9-34,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 9-34,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 9-34,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 9-34,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 9-34,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 9-34,...Ch. 5.4 - Prob. 19ECh. 5.4 - Prob. 20ECh. 5.4 - Evaluating a Definite Integral In Exercises 9-34,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 9-34,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 9-34,...Ch. 5.4 - Prob. 24ECh. 5.4 - Prob. 25ECh. 5.4 - Evaluating a Definite Integral In Exercises 9-34,...Ch. 5.4 - Prob. 27ECh. 5.4 - Evaluating a Definite Integral In Exercises 9-34,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 9-34,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 9-34,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 9-34,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 9-34,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 9-34,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 9-34,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 9-34,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 9-34,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 9-34,...Ch. 5.4 - Evaluating a Definite Integral In Exercises 9-34,...Ch. 5.4 - Finding the Area of a Region In Exercises 35-38,...Ch. 5.4 - Finding the Area of a Region In Exercises 35-38,...Ch. 5.4 - Finding the Area of a Region In Exercises 35-38,...Ch. 5.4 - Finding the Area of a Region In Exercises 35-38,...Ch. 5.4 - Finding the Area of a Region In Exercises 39-44,...Ch. 5.4 - Finding the Area of a Region In Exercises 39-44,...Ch. 5.4 - Finding the Area of a Region In Exercises 39-44,...Ch. 5.4 - Finding the Area of a Region In Exercises 39-44,...Ch. 5.4 - Finding the Area of a Region In Exercises 39-44,...Ch. 5.4 - Finding the Area of a Region In Exercises 39-44,...Ch. 5.4 - Using the Mean Value Theorem for Integrals In...Ch. 5.4 - Using the Mean Value Theorem for Integrals In...Ch. 5.4 - Using the Mean Value Theorem for Integrals In...Ch. 5.4 - Prob. 52ECh. 5.4 - Prob. 53ECh. 5.4 - Prob. 54ECh. 5.4 - Prob. 55ECh. 5.4 - Prob. 56ECh. 5.4 - Prob. 57ECh. 5.4 - Prob. 58ECh. 5.4 - Prob. 59ECh. 5.4 - Prob. 60ECh. 5.4 - Using a Graph The graph of f is shown in the...Ch. 5.4 - Prob. 64ECh. 5.4 - Prob. 65ECh. 5.4 - Prob. 66ECh. 5.4 - Prob. 115ECh. 5.4 - HOW DO YOU SEE IT? The graph of f is shown in the...Ch. 5.4 - Prob. 67ECh. 5.4 - Average Sales A company fits a model to the...Ch. 5.4 - Prob. 71ECh. 5.4 - Prob. 72ECh. 5.4 - Prob. 73ECh. 5.4 - Prob. 74ECh. 5.4 - Prob. 75ECh. 5.4 - Prob. 76ECh. 5.4 - Prob. 77ECh. 5.4 - Analyzing a Function Let g(x)=0xf(t)dt, where f is...Ch. 5.4 - Prob. 79ECh. 5.4 - Prob. 80ECh. 5.4 - Prob. 81ECh. 5.4 - Prob. 82ECh. 5.4 - Prob. 83ECh. 5.4 - Finding and Checking an Integral In Exercises...Ch. 5.4 - Prob. 85ECh. 5.4 - Prob. 86ECh. 5.4 - Prob. 87ECh. 5.4 - Prob. 88ECh. 5.4 - Prob. 89ECh. 5.4 - Prob. 90ECh. 5.4 - Prob. 91ECh. 5.4 - Using the Second Fundamental Theorem of Calculus...Ch. 5.4 - Finding a Derivative In Exercises 81-86, find...Ch. 5.4 - Prob. 94ECh. 5.4 - Finding a Derivative In Exercises 81-86, find...Ch. 5.4 - Prob. 96ECh. 5.4 - Finding a Derivative In Exercises 81-86, find...Ch. 5.4 - Prob. 98ECh. 5.4 - Graphical Analysis Sketch an approximate graph or...Ch. 5.4 - Prob. 100ECh. 5.4 - Water Flow Water flows from a storage tank at a...Ch. 5.4 - Oil Leak At 1:00 p.m., oil begins leaking from a...Ch. 5.4 - Velocity The graph shows the velocity, in feet per...Ch. 5.4 - Velocity The graph shows the velocity, in feet per...Ch. 5.4 - Prob. 101ECh. 5.4 - Particle Motion In Exercises 93-98, the velocity...Ch. 5.4 - Particle Motion In Exercises 93-98, the velocity...Ch. 5.4 - Prob. 104ECh. 5.4 - Particle Motion In Exercises 93-98, the velocity...Ch. 5.4 - Particle Motion In Exercises 93-98, the velocity...Ch. 5.4 - Prob. 69ECh. 5.4 - Prob. 107ECh. 5.4 - Prob. 108ECh. 5.4 - Error Analysis In Exercises 105-108, describe why...Ch. 5.4 - Prob. 112ECh. 5.4 - Prob. 113ECh. 5.4 - Prob. 114ECh. 5.4 - Prob. 117ECh. 5.4 - Prob. 118ECh. 5.4 - Prob. 119ECh. 5.4 - Prob. 120ECh. 5.4 - Prob. 121ECh. 5.4 - Prob. 116ECh. 5.5 - Finding uand du In Exercises 14, complete the...Ch. 5.5 - Prob. 2ECh. 5.5 - Prob. 3ECh. 5.5 - Prob. 4ECh. 5.5 - Prob. 5ECh. 5.5 - Finding an Indefinite Integral In Exercises 9-28,...Ch. 5.5 - Finding an Indefinite Integral In Exercises 9-28,...Ch. 5.5 - Prob. 8ECh. 5.5 - Finding an Indefinite Integral In Exercises 9-28,...Ch. 5.5 - Finding an Indefinite Integral In Exercises 9-28,...Ch. 5.5 - Prob. 11ECh. 5.5 - Finding an Indefinite Integral In Exercises 9-28,...Ch. 5.5 - Finding an Indefinite Integral In Exercises 9-28,...Ch. 5.5 - Prob. 14ECh. 5.5 - Finding an Indefinite Integral In Exercises 9-28,...Ch. 5.5 - Prob. 16ECh. 5.5 - Prob. 17ECh. 5.5 - Prob. 18ECh. 5.5 - Prob. 19ECh. 5.5 - Finding an Indefinite Integral In Exercises 9-28,...Ch. 5.5 - Finding an Indefinite Integral In Exercises 9-28,...Ch. 5.5 - Finding an Indefinite Integral In Exercises 9-28,...Ch. 5.5 - Finding an Indefinite Integral In Exercises 9-28,...Ch. 5.5 - Prob. 24ECh. 5.5 - Prob. 25ECh. 5.5 - Prob. 26ECh. 5.5 - Prob. 27ECh. 5.5 - Differential Equation In Exercises 29-32, find the...Ch. 5.5 - Differential Equation In Exercises 29-32, find the...Ch. 5.5 - Prob. 30ECh. 5.5 - Prob. 31ECh. 5.5 - Slope Field In Exercises 33 and 34, a differential...Ch. 5.5 - Prob. 33ECh. 5.5 - Finding an Indefinite Integral In Exercises 35-56,...Ch. 5.5 - Finding an Indefinite Integral In Exercises 35-56,...Ch. 5.5 - Finding an Indefinite Integral In Exercises 35-56,...Ch. 5.5 - Finding an Indefinite Integral In Exercises 35-56,...Ch. 5.5 - Finding an Indefinite Integral In Exercises 35-56,...Ch. 5.5 - Prob. 39ECh. 5.5 - Finding an Indefinite Integral In Exercises 35-56,...Ch. 5.5 - Prob. 41ECh. 5.5 - Finding an Indefinite Integral In Exercises 35-56,...Ch. 5.5 - Finding an Indefinite Integral In Exercises 35-56,...Ch. 5.5 - Finding an Indefinite Integral In Exercises 35-56,...Ch. 5.5 - Prob. 45ECh. 5.5 - Prob. 46ECh. 5.5 - Prob. 47ECh. 5.5 - Prob. 48ECh. 5.5 - Prob. 49ECh. 5.5 - Finding an Indefinite Integral In Exercises 35-56,...Ch. 5.5 - Finding an Indefinite Integral In Exercises 35-56,...Ch. 5.5 - Finding an Indefinite Integral In Exercises 35-56,...Ch. 5.5 - Finding an Indefinite Integral In Exercises 35-56,...Ch. 5.5 - Prob. 54ECh. 5.5 - Prob. 59ECh. 5.5 - Finding an Equation In Exercises 57-64, find an...Ch. 5.5 - Prob. 55ECh. 5.5 - Prob. 58ECh. 5.5 - Prob. 56ECh. 5.5 - Prob. 57ECh. 5.5 - Change of Variables In Exercises 65-72, find the...Ch. 5.5 - Change of Variables In Exercises 65-72, find the...Ch. 5.5 - Prob. 63ECh. 5.5 - Change of Variables In Exercises 65-72, find the...Ch. 5.5 - Prob. 65ECh. 5.5 - Prob. 66ECh. 5.5 - Change of Variables In Exercises 6168, find the...Ch. 5.5 - Prob. 68ECh. 5.5 - Prob. 69ECh. 5.5 - Evaluating a Definite Integral In Exercises 73-84,...Ch. 5.5 - Evaluating a Definite Integral In Exercises 73-84,...Ch. 5.5 - Evaluating a Definite Integral In Exercises 73-84,...Ch. 5.5 - Evaluating a Definite Integral In Exercises 73-84,...Ch. 5.5 - Evaluating a Definite Integral In Exercises 73-84,...Ch. 5.5 - Prob. 75ECh. 5.5 - Prob. 76ECh. 5.5 - Prob. 77ECh. 5.5 - Evaluating a Definite Integral In Exercises 73-84,...Ch. 5.5 - Prob. 79ECh. 5.5 - Evaluating a Definite Integral In Exercises 73-84,...Ch. 5.5 - Prob. 81ECh. 5.5 - Prob. 82ECh. 5.5 - Prob. 83ECh. 5.5 - Prob. 84ECh. 5.5 - Prob. 85ECh. 5.5 - Area In Exercises 89-92, find the area of the...Ch. 5.5 - Prob. 87ECh. 5.5 - Area In Exercises 89-92, find the area of the...Ch. 5.5 - Prob. 89ECh. 5.5 - Prob. 90ECh. 5.5 - Prob. 91ECh. 5.5 - Even and Odd Functions In Exercises 93-96,...Ch. 5.5 - Prob. 93ECh. 5.5 - Prob. 94ECh. 5.5 - Even and Odd Functions In Exercises 99 and 100,...Ch. 5.5 - Prob. 96ECh. 5.5 - WRITING ABOUT CONCEPTS Using Substitution Describe...Ch. 5.5 - Prob. 98ECh. 5.5 - Prob. 99ECh. 5.5 - Prob. 100ECh. 5.5 - Depreciation The rate of depreciation dV/dt of a...Ch. 5.5 - HOW DO YOU SEE IT? The graph shows the flow rate...Ch. 5.5 - Prob. 103ECh. 5.5 - Prob. 104ECh. 5.5 - Prob. 107ECh. 5.5 - The probability that a person will remember...Ch. 5.5 - The probability that ore samples taken from a...Ch. 5.5 - Prob. 108ECh. 5.5 - Prob. 109ECh. 5.5 - Rewriting Integral (a) Show that...Ch. 5.5 - Prob. 111ECh. 5.5 - Prob. 112ECh. 5.5 - Prob. 113ECh. 5.5 - Prob. 114ECh. 5.5 - Prob. 115ECh. 5.5 - Prob. 116ECh. 5.5 - Prob. 117ECh. 5.5 - Prob. 118ECh. 5.5 - Prob. 119ECh. 5.5 - Prob. 120ECh. 5.5 - Prob. 121ECh. 5.5 - Prob. 122ECh. 5.6 - Prob. 1ECh. 5.6 - Prob. 2ECh. 5.6 - Prob. 3ECh. 5.6 - Prob. 4ECh. 5.6 - Prob. 5ECh. 5.6 - Prob. 6ECh. 5.6 - Prob. 7ECh. 5.6 - Prob. 8ECh. 5.6 - Prob. 9ECh. 5.6 - Prob. 10ECh. 5.6 - Prob. 11ECh. 5.6 - Prob. 12ECh. 5.6 - Prob. 13ECh. 5.6 - Prob. 14ECh. 5.6 - Prob. 15ECh. 5.6 - Prob. 16ECh. 5.6 - Prob. 17ECh. 5.6 - Prob. 18ECh. 5.6 - Prob. 19ECh. 5.6 - Prob. 20ECh. 5.6 - Prob. 21ECh. 5.6 - Prob. 22ECh. 5.6 - Prob. 23ECh. 5.6 - Prob. 24ECh. 5.6 - Prob. 25ECh. 5.6 - Prob. 26ECh. 5.6 - Prob. 27ECh. 5.6 - Prob. 28ECh. 5.6 - Prob. 29ECh. 5.6 - Prob. 30ECh. 5.6 - Prob. 31ECh. 5.6 - Prob. 32ECh. 5.6 - Estimating Errors Using Technology In Exercises...Ch. 5.6 - Estimating Errors Using Technology In Exercises...Ch. 5.6 - Estimating Errors Using Technology In Exercises...Ch. 5.6 - Estimating Errors Using Technology In Exercises...Ch. 5.6 - Finding the Area of a Region Approximate the area...Ch. 5.6 - Prob. 38ECh. 5.6 - Prob. 39ECh. 5.6 - Circumference The elliptic...Ch. 5.6 - Prob. 41ECh. 5.6 - HOW DO YOU SEE IT? The function f(x) is concave...Ch. 5.6 - Prob. 43ECh. 5.6 - Prob. 44ECh. 5.6 - Prob. 45ECh. 5.6 - Prob. 46ECh. 5.6 - Prob. 47ECh. 5.6 - Prob. 48ECh. 5.6 - Prob. 49ECh. 5.7 - Finding an Indefinite Integral In Exercises 5-28,...Ch. 5.7 - Prob. 2ECh. 5.7 - Prob. 3ECh. 5.7 - Prob. 4ECh. 5.7 - Prob. 5ECh. 5.7 - Finding an Indefinite Integral In Exercises 5-28,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 5-28,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 5-28,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 5-28,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 5-28,...Ch. 5.7 - Prob. 11ECh. 5.7 - Finding an Indefinite Integral In Exercises 5-28,...Ch. 5.7 - Prob. 13ECh. 5.7 - Finding an Indefinite Integral In Exercises 5-28,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 5-28,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 5-28,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 5-28,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 5-28,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 5-28,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 5-28,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 5-28,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 5-28,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 5-28,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 5-28,...Ch. 5.7 - Prob. 25ECh. 5.7 - Prob. 26ECh. 5.7 - Prob. 27ECh. 5.7 - Prob. 28ECh. 5.7 - Change of Variables In Exercises 29-32, find the...Ch. 5.7 - Prob. 30ECh. 5.7 - Prob. 31ECh. 5.7 - Prob. 34ECh. 5.7 - Prob. 32ECh. 5.7 - Prob. 33ECh. 5.7 - Prob. 35ECh. 5.7 - Prob. 36ECh. 5.7 - Prob. 37ECh. 5.7 - Finding an Indefinite Integral of a Trigonometric...Ch. 5.7 - Prob. 39ECh. 5.7 - Prob. 40ECh. 5.7 - Prob. 41ECh. 5.7 - Prob. 42ECh. 5.7 - Differential Equation In Exercises 43-46, find the...Ch. 5.7 - Differential Equation In Exercises 43-46, find the...Ch. 5.7 - Prob. 45ECh. 5.7 - Prob. 46ECh. 5.7 - Prob. 47ECh. 5.7 - Finding a Particular Solution In Exercises 47 and...Ch. 5.7 - Prob. 49ECh. 5.7 - Prob. 50ECh. 5.7 - Prob. 51ECh. 5.7 - Prob. 52ECh. 5.7 - Evaluating a Definite Integral In Exercises 51-58,...Ch. 5.7 - Evaluating a Definite Integral In Exercises 51-58,...Ch. 5.7 - Evaluating a Definite Integral In Exercises 51-58,...Ch. 5.7 - Prob. 56ECh. 5.7 - Prob. 57ECh. 5.7 - Prob. 58ECh. 5.7 - Prob. 60ECh. 5.7 - Prob. 64ECh. 5.7 - Prob. 59ECh. 5.7 - Prob. 61ECh. 5.7 - Prob. 62ECh. 5.7 - Prob. 63ECh. 5.7 - Prob. 65ECh. 5.7 - Prob. 66ECh. 5.7 - Prob. 67ECh. 5.7 - Prob. 68ECh. 5.7 - Prob. 69ECh. 5.7 - Prob. 70ECh. 5.7 - Prob. 71ECh. 5.7 - Prob. 72ECh. 5.7 - Prob. 73ECh. 5.7 - Prob. 74ECh. 5.7 - Prob. 75ECh. 5.7 - Prob. 76ECh. 5.7 - Prob. 95ECh. 5.7 - Prob. 96ECh. 5.7 - Prob. 97ECh. 5.7 - Prob. 98ECh. 5.7 - Prob. 77ECh. 5.7 - Prob. 78ECh. 5.7 - Prob. 79ECh. 5.7 - Prob. 80ECh. 5.7 - Prob. 81ECh. 5.7 - Prob. 82ECh. 5.7 - Prob. 83ECh. 5.7 - Prob. 84ECh. 5.7 - Prob. 85ECh. 5.7 - Prob. 86ECh. 5.7 - Prob. 87ECh. 5.7 - Prob. 88ECh. 5.7 - Prob. 89ECh. 5.7 - Prob. 90ECh. 5.7 - Prob. 91ECh. 5.7 - Prob. 92ECh. 5.7 - Prob. 93ECh. 5.7 - Prob. 94ECh. 5.7 - Prob. 99ECh. 5.7 - Sales The rate of change in sales S is inversely...Ch. 5.7 - Prob. 101ECh. 5.7 - Prob. 102ECh. 5.7 - Prob. 103ECh. 5.7 - Prob. 104ECh. 5.7 - Prob. 105ECh. 5.7 - Prob. 106ECh. 5.7 - Prob. 107ECh. 5.7 - Prob. 108ECh. 5.7 - Prob. 109ECh. 5.7 - Prob. 110ECh. 5.7 - Prob. 111ECh. 5.8 - Prob. 1ECh. 5.8 - Prob. 2ECh. 5.8 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.8 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.8 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.8 - Prob. 6ECh. 5.8 - Prob. 7ECh. 5.8 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.8 - Prob. 9ECh. 5.8 - Prob. 10ECh. 5.8 - Prob. 11ECh. 5.8 - Prob. 12ECh. 5.8 - Prob. 13ECh. 5.8 - Prob. 14ECh. 5.8 - Prob. 15ECh. 5.8 - Prob. 16ECh. 5.8 - Prob. 17ECh. 5.8 - Prob. 18ECh. 5.8 - Prob. 19ECh. 5.8 - Prob. 20ECh. 5.8 - Prob. 21ECh. 5.8 - Prob. 22ECh. 5.8 - Prob. 23ECh. 5.8 - Prob. 24ECh. 5.8 - Prob. 25ECh. 5.8 - Prob. 26ECh. 5.8 - Prob. 27ECh. 5.8 - Prob. 28ECh. 5.8 - Prob. 29ECh. 5.8 - Prob. 30ECh. 5.8 - Prob. 31ECh. 5.8 - Prob. 32ECh. 5.8 - Prob. 33ECh. 5.8 - Prob. 34ECh. 5.8 - Prob. 35ECh. 5.8 - Prob. 36ECh. 5.8 - Prob. 37ECh. 5.8 - Prob. 38ECh. 5.8 - Prob. 39ECh. 5.8 - Completing the Square In Exercises 35-42, Find or...Ch. 5.8 - Prob. 41ECh. 5.8 - Prob. 42ECh. 5.8 - Prob. 43ECh. 5.8 - Prob. 44ECh. 5.8 - Prob. 45ECh. 5.8 - Prob. 46ECh. 5.8 - Prob. 47ECh. 5.8 - Prob. 48ECh. 5.8 - Comparing Integration Problems In Exercises 47-50,...Ch. 5.8 - Prob. 50ECh. 5.8 - Prob. 51ECh. 5.8 - Prob. 52ECh. 5.8 - Prob. 55ECh. 5.8 - Prob. 56ECh. 5.8 - Prob. 57ECh. 5.8 - Prob. 58ECh. 5.8 - Prob. 59ECh. 5.8 - Prob. 60ECh. 5.8 - Prob. 53ECh. 5.8 - Prob. 54ECh. 5.8 - Prob. 61ECh. 5.8 - Area In Exercises 63-66, find the area of the...Ch. 5.8 - Prob. 63ECh. 5.8 - Prob. 64ECh. 5.8 - Prob. 65ECh. 5.8 - Prob. 66ECh. 5.8 - Prob. 67ECh. 5.8 - Prob. 68ECh. 5.8 - Prob. 69ECh. 5.8 - Prob. 70ECh. 5.8 - Prob. 71ECh. 5.8 - Prob. 72ECh. 5.8 - Prob. 73ECh. 5.8 - Prob. 74ECh. 5.8 - Prob. 75ECh. 5.8 - Prob. 76ECh. 5.8 - Prob. 77ECh. 5.8 - Prob. 78ECh. 5.8 - Prob. 79ECh. 5.8 - Prob. 80ECh. 5.9 - Prob. 1ECh. 5.9 - Evaluating a Function In Exercises 5-10, evaluate...Ch. 5.9 - Evaluating a Function In Exercises 5-10, evaluate...Ch. 5.9 - Prob. 4ECh. 5.9 - Evaluating a Function In Exercises 5-10, evaluate...Ch. 5.9 - Prob. 6ECh. 5.9 - Verifying an Identity In Exercises 11-18, verify...Ch. 5.9 - Verifying an Identity In Exercises 11-18, verify...Ch. 5.9 - Prob. 9ECh. 5.9 - Prob. 10ECh. 5.9 - Prob. 11ECh. 5.9 - Prob. 12ECh. 5.9 - Prob. 13ECh. 5.9 - Prob. 14ECh. 5.9 - Prob. 15ECh. 5.9 - Prob. 16ECh. 5.9 - Prob. 17ECh. 5.9 - Prob. 18ECh. 5.9 - Prob. 19ECh. 5.9 - Prob. 20ECh. 5.9 - Prob. 21ECh. 5.9 - Prob. 22ECh. 5.9 - Prob. 23ECh. 5.9 - Finding a Derivative In Exercises 25-34, find the...Ch. 5.9 - Prob. 25ECh. 5.9 - Finding a Derivative In Exercises 25-34, find the...Ch. 5.9 - Prob. 27ECh. 5.9 - Finding a Derivative In Exercises 25-34, find the...Ch. 5.9 - Prob. 29ECh. 5.9 - Prob. 30ECh. 5.9 - Prob. 31ECh. 5.9 - Finding a Derivative In Exercises 25-34, find the...Ch. 5.9 - Finding a Derivative In Exercises 25-34, find the...Ch. 5.9 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.9 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.9 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.9 - Finding Relative Extrema In Exercises 39-42, find...Ch. 5.9 - Finding Relative Extrema In Exercises 39-42, find...Ch. 5.9 - Finding Relative Extrema In Exercises 39-42, find...Ch. 5.9 - Finding Relative Extrema In Exercises 39-42, find...Ch. 5.9 - Catenary In Exercises 43 and 44, a model for a...Ch. 5.9 - Catenary In Exercises 43 and 44, a model for a...Ch. 5.9 - Prob. 43ECh. 5.9 - Finding an Indefinite Integral In Exercises 45-54,...Ch. 5.9 - Finding an Indefinite Integral In Exercises 45-54,...Ch. 5.9 - Prob. 46ECh. 5.9 - Finding an Indefinite Integral In Exercises 45-54,...Ch. 5.9 - Finding an Indefinite Integral In Exercises 45-54,...Ch. 5.9 - Finding an Indefinite Integral In Exercises 45-54,...Ch. 5.9 - Prob. 50ECh. 5.9 - Finding an Indefinite Integral In Exercises 45-54,...Ch. 5.9 - Prob. 51ECh. 5.9 - Prob. 52ECh. 5.9 - Prob. 54ECh. 5.9 - Prob. 55ECh. 5.9 - Prob. 56ECh. 5.9 - Prob. 57ECh. 5.9 - Prob. 58ECh. 5.9 - Prob. 59ECh. 5.9 - Prob. 60ECh. 5.9 - Prob. 61ECh. 5.9 - Prob. 62ECh. 5.9 - Prob. 63ECh. 5.9 - HOW DO YOU SEE IT? Use the graphs of f and g shown...Ch. 5.9 - Prob. 65ECh. 5.9 - Prob. 66ECh. 5.9 - Prob. 67ECh. 5.9 - Finding a Derivative In Exercises 65-74, find the...Ch. 5.9 - Finding a Derivative In Exercises 65-74, find the...Ch. 5.9 - Finding a Derivative In Exercises 65-74, find the...Ch. 5.9 - Prob. 71ECh. 5.9 - Prob. 72ECh. 5.9 - Prob. 73ECh. 5.9 - Prob. 74ECh. 5.9 - Prob. 75ECh. 5.9 - Prob. 76ECh. 5.9 - Prob. 77ECh. 5.9 - Prob. 78ECh. 5.9 - Prob. 79ECh. 5.9 - Prob. 80ECh. 5.9 - Prob. 81ECh. 5.9 - Prob. 82ECh. 5.9 - Prob. 83ECh. 5.9 - Prob. 84ECh. 5.9 - Prob. 85ECh. 5.9 - Prob. 86ECh. 5.9 - Prob. 87ECh. 5.9 - Prob. 88ECh. 5.9 - Prob. 89ECh. 5.9 - Prob. 90ECh. 5.9 - Prob. 91ECh. 5.9 - Prob. 92ECh. 5.9 - Prob. 93ECh. 5.9 - Prob. 94ECh. 5.9 - Prob. 95ECh. 5.9 - Prob. 96ECh. 5.9 - Prob. 97ECh. 5.9 - Prob. 98ECh. 5.9 - Proof Prove that tanh1x=12ln(1+x1x),1x1Ch. 5.9 - Prob. 100ECh. 5.9 - Prob. 101ECh. 5.9 - Prob. 102ECh. 5.9 - Prob. 103ECh. 5.9 - Prob. 104ECh. 5.9 - Prob. 105ECh. 5.9 - Prob. 106ECh. 5.9 - Prob. 107ECh. 5.9 - Prob. 108ECh. 5.9 - Prob. 109ECh. 5.9 - PUTNAM EXAM CHALLENGE Prove or disprove: there is...Ch. 5 - Finding an Indefinite Integral In Exercises 1-6,...Ch. 5 - Finding an Indefinite Integral In Exercises 1-6,...Ch. 5 - Finding an Indefinite Integral In Exercises 1-6,...Ch. 5 - Finding an Indefinite Integral In Exercises 1-6,...Ch. 5 - Finding an Indefinite Integral In Exercises 1-6,...Ch. 5 - Prob. 6RECh. 5 - Prob. 7RECh. 5 - Prob. 8RECh. 5 - Finding a Particular Solution In Exercises 7-10,...Ch. 5 - Finding a Particular Solution In Exercises 7-10,...Ch. 5 - Vertical Motion A ball is thrown vertically upward...Ch. 5 - Vertical Motion With what initial velocity must an...Ch. 5 - Prob. 13RECh. 5 - Prob. 14RECh. 5 - Prob. 15RECh. 5 - Prob. 16RECh. 5 - Evaluating a Sum In Exercises 17-20, use the...Ch. 5 - Evaluating a Sum In Exercises 17-20, use the...Ch. 5 - Evaluating a Sum In Exercises 17-20, use the...Ch. 5 - Prob. 20RECh. 5 - Prob. 21RECh. 5 - Prob. 22RECh. 5 - Prob. 23RECh. 5 - Prob. 24RECh. 5 - Prob. 25RECh. 5 - Prob. 26RECh. 5 - Evaluating a Definite Integral Using a Geometric...Ch. 5 - Prob. 28RECh. 5 - Using Properties of Definite Integrals Given...Ch. 5 - Prob. 30RECh. 5 - Evaluating a Definite Integral In Exercises 35-40,...Ch. 5 - Evaluating a Definite Integral In Exercises 35-40,...Ch. 5 - Evaluating a Definite Integral In Exercises 35-40,...Ch. 5 - Prob. 34RECh. 5 - Evaluating a Definite Integral In Exercises 35-40,...Ch. 5 - Prob. 36RECh. 5 - Finding the Area of a Region In Exercises 41-44,...Ch. 5 - Prob. 38RECh. 5 - Finding the Area of a Region In Exercises 41-44,...Ch. 5 - Prob. 40RECh. 5 - Finding the Average Value of a Function In...Ch. 5 - Prob. 42RECh. 5 - Using the Second Fundamental Theorem of Calculus...Ch. 5 - Prob. 44RECh. 5 - Prob. 45RECh. 5 - Using the Second Fundamental Theorem of Calculus...Ch. 5 - Prob. 47RECh. 5 - Prob. 48RECh. 5 - Prob. 49RECh. 5 - Prob. 50RECh. 5 - Prob. 51RECh. 5 - Prob. 52RECh. 5 - Prob. 53RECh. 5 - Prob. 54RECh. 5 - Prob. 55RECh. 5 - Prob. 56RECh. 5 - Prob. 57RECh. 5 - Prob. 58RECh. 5 - Prob. 59RECh. 5 - Prob. 60RECh. 5 - Prob. 61RECh. 5 - Prob. 62RECh. 5 - Prob. 63RECh. 5 - Evaluating a Definite Integral In Exercises 63-70,...Ch. 5 - Evaluating a Definite Integral In Exercises 63-70,...Ch. 5 - Evaluating a Definite Integral In Exercises 63-70,...Ch. 5 - Evaluating a Definite Integral In Exercises 63-70,...Ch. 5 - Evaluating a Definite Integral In Exercises 63-70,...Ch. 5 - Prob. 69RECh. 5 - Prob. 70RECh. 5 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 5 - Prob. 72RECh. 5 - Finding an Indefinite Integral In Exercises 79-84,...Ch. 5 - Finding an Indefinite Integral In Exercises 79-84,...Ch. 5 - Finding an Indefinite Integral In Exercises 79-84,...Ch. 5 - Prob. 76RECh. 5 - Prob. 77RECh. 5 - Prob. 78RECh. 5 - Evaluating a Definite Integral In Exercises 85-88,...Ch. 5 - Evaluating a Definite Integral In Exercises 85-88,...Ch. 5 - Evaluating a Definite Integral In Exercises 85-88,...Ch. 5 - Evaluating a Definite Integral In Exercises 85-88,...Ch. 5 - Prob. 83RECh. 5 - Finding an Indefinite Integral In Exercises 89-94,...Ch. 5 - Prob. 85RECh. 5 - Prob. 86RECh. 5 - Prob. 87RECh. 5 - Prob. 88RECh. 5 - Prob. 89RECh. 5 - Finding a Derivative In Exercises 95-98, find the...Ch. 5 - Prob. 91RECh. 5 - Prob. 92RECh. 5 - Prob. 93RECh. 5 - Prob. 94RECh. 5 - Prob. 95RECh. 5 - Prob. 96RECh. 5 - Prob. 1PSCh. 5 - Prob. 2PSCh. 5 - Prob. 3PSCh. 5 - Prob. 4PSCh. 5 - Approximation The Two-Point Gaussian Quadrature...Ch. 5 - Prob. 6PSCh. 5 - Prob. 7PSCh. 5 - Prob. 8PSCh. 5 - Prob. 9PSCh. 5 - Prob. 10PSCh. 5 - Prob. 11PSCh. 5 - Prob. 12PSCh. 5 - Velocity and Acceleration A car travels in a...Ch. 5 - Prob. 14PSCh. 5 - Prob. 15PSCh. 5 - Area Consider the three regions A, B. and C...Ch. 5 - Prob. 17PSCh. 5 - Prob. 18PSCh. 5 - Prob. 19PS
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY