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Math
Calculus
Calculus: Early Transcendentals, Loose-leaf Version, 9th
Chapter 5.2, Problem 2DP
Chapter 5.2, Problem 2DP
BUY
Calculus: Early Transcendentals, Loose-leaf Version, 9th
9th Edition
ISBN:
9780357022290
Author: Stewart
Publisher:
Cengage Learning Acquisitions
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1 Functions And Models
2 Limits And Derivatives
3 Differentiation Rules
4 Applications Of Differentiation
5 Integrals
6 Applications Of Integration
7 Techniques Of Integration
8 Further Applications Of Integration
9 Differential Equations
10 Parametric Equations And Polar Coordinates
11 Sequences, Series, And Power Series
12 Vectors And The Geometry Of Space
13 Vector Functions
14 Partial Derivatives
15 Multiple Integrals
16 Vector Calculus
A Numbers, Inequalities, And Absolute Values
B Coordinate Geometry And Lines
C Graphs Of Second-degree Equations
D Trigonometry
E Sigma Notation
F Proofs Of Theorems
G The Logarithm Defined As An Integral
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5.1 The Area And Distance Problems
5.2 The Definite Integral
5.3 The Fundamental Theorem Of Calculus
5.4 Indefinite Integrals And The Net Change Theorem
5.5 The Substitution Rule
Chapter Questions
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Problem 1E: Evaluate the Riemann sum for f(x) = x 1, 6 x 4, with five subintervals, taking the sample points...
Problem 2E: If f(x)=cosx0x3/4 evaluate the Riemann sum with n = 6, taking the sample points to be left...
Problem 3E: If f(x) = x2 4, 0 x 3, find the Riemann sum with n = 6, taking the sample points to be midpoints....
Problem 4E
Problem 5E
Problem 6E: The graph of a function g is shown. Estimate 24g(x)dx with six subintervals using (a) right...
Problem 7E: A table of values of an increasing function f is shown. Use the table to find lower and upper...
Problem 8E: The table gives the values of a function obtained from an experiment. Use them to estimate 39f(x)dx...
Problem 9E: Use the Midpoint Rule with n=4 to approximate the integral. 9. 08x2dx
Problem 10E: Use the Midpoint Rule with n=4 to approximate the integral. 10. 02(8x+3)dx
Problem 11E
Problem 12E: Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to...
Problem 13E: Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to...
Problem 14E: Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to...
Problem 15E
Problem 16E
Problem 17E
Problem 18E: Use a calculator or computer to make a table of values of left and right Riemann sums Ln and Rn for...
Problem 19E: Express the limit as a definite integral on the given interval. limni=1nexi1+xix,[0,1]
Problem 20E: Express the limit as a definite integral on the given interval. limni=1nxi1+xi3x,[2,5]
Problem 21E: Express the limit as a definite integral on the given interval. limni=1n[5(xi)34xi]x,[2,7]
Problem 22E: Express the limit as a definite integral on the given interval. limni=1nxi(xi)2+4x,[1,3]
Problem 23E: Show that the definite integral is equal to lim n R n and then evaluate the limit. 23. 0 4 x x 2...
Problem 24E
Problem 25E
Problem 26E
Problem 27E: Use the form of the definition of the integral given in Theorem 4 to evaluate the integral. 27....
Problem 28E: Use the form of the definition of the integral given in Theorem 4 to evaluate the integral. 28....
Problem 29E
Problem 30E
Problem 31E: Use the form of the definition of the integral given in Theorem 4 to evaluate the integral. 31....
Problem 32E
Problem 33E: Use the form of the definition of the integral given in Theorem 4 to evaluate the integral....
Problem 34E: Use the form of the definition of the integral given in Theorem 4 to evaluate the integral....
Problem 35E
Problem 36E: The graph of g consists of two straight lines and a semicircle. Evaluate each integral by...
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E: Evaluate the integral by interpreting it in terms of areas. 41. 25(105x)dx
Problem 42E: Evaluate the integral by interpreting it in terms of areas. 42. 13(2x1)dx
Problem 43E: Evaluate the integral by interpreting it in terms of areas. 43. 4312xdx
Problem 44E
Problem 45E: Evaluate the integral by interpreting it in terms of areas. 45. 301+9x2dx
Problem 46E: Evaluate the integral by interpreting it in terms of areas. 46. 442x16x2dx
Problem 47E
Problem 48E
Problem 49E
Problem 50E
Problem 51E: Evaluate 111+x4dx.
Problem 52E: Given that 0sin4xdx=83, what is 0sin4d?
Problem 53E: In Example 5.1.2 we showed that 01x2dx13. Use this fact and the properties of integrals to evaluate...
Problem 54E: Use the properties of integrals and the result of Example 3 to evaluate 13(2ex1)dx.
Problem 55E
Problem 56E
Problem 57E: Write as a single integral in the form abf(x)dx: 22f(x)dx+25f(x)dx21f(x)dx
Problem 58E: If 28f(x)dx=7.3 and 24f(x)dx=5.9, find 48f(x)dx.
Problem 59E: If 09f(x)dx=37 and 09g(x)dx=16, find 09[2f(x)+3g(x)]dx
Problem 60E: Find 05f(x)dx if f(x)={3forx3xforx3
Problem 61E: For the function f whose graph is shown, list the following quantities in increasing order, from...
Problem 62E: If , F(x)=2xf(t)dt, where f is the function whose graph is given, which of the following values is...
Problem 63E: Each of the regions A, B, and C bounded by the graph of f and the x-axis has area 3. Find the value...
Problem 64E: Suppose f has absolute minimum value m and absolute maximum value M. Between what two values must...
Problem 65E: Use the properties of integrals to verify the inequality without evaluating the integrals....
Problem 66E: Use the properties of integrals to verify the inequality without evaluating the integrals....
Problem 67E: Use the properties of integrals to verify the inequality without evaluating the integrals....
Problem 68E: Use the properties of integrals to verify the inequality without evaluating the integrals....
Problem 69E: Use Property 8 to estimate the value of the integral. 01x3dx
Problem 70E: Use Property 8 to estimate the value of the integral. 031x+4dx
Problem 71E: Use Property 8 to estimate the value of the integral. /4/3tanxdx
Problem 72E: Use Property 8 to estimate the value of the integral. 02(x33x+3)dx
Problem 73E: Use Property 8 to estimate the value of the integral. 02xexdx
Problem 74E: Use Property 8 to estimate the value of the integral. 2(x2sinx)dx
Problem 75E: Use properties of integrals, together with Exercises 27 and 28, to prove the inequality. 13x4+1dx263
Problem 76E: Use properties of integrals, together with Exercises 27 and 28, to prove the inequality....
Problem 77E: Which of the integrals 12arctanxdx, 12arctanxdx, and 12arctan(sinx)dx has the largest value? Why?
Problem 78E: Which of the integrals 00.5cos(x2)dx, 00.5cosxdx is larger? Why?
Problem 79E
Problem 80E
Problem 81E: Let f(x) = 0 if x is any rational number and f(x) = 1 if x is any irrational number. Show that f is...
Problem 82E: Let f(0) = 0 and f(x) = 1/x if 0 x 1. Show that f is not integrable on [0, 1]. [Hint: Show that...
Problem 83E: Express the limit as a definite integral. limni=1ni4n5 [Hint: Consider f(x) = x4.]
Problem 84E: Express the limit as a definite integral. limn1ni=1n11+(i/n)2
Problem 85E: Find 12x2dx. Hint: Choose xi to be the geometric mean of xi1 and xi (thatis,xi=xi1xi) and use the...
Problem 1DP
Problem 2DP
Problem 3DP: (a) Draw the graph of the function f(x)=cosx2 in the viewing rectangle 0,2 by [1.25,1.25] . (b) If...
Problem 4DP
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