Consider the function f (x) = 5 cos x. What is the estimate of the area under the curve of f using rectangular approximations and sample points on the interval [-1. 5, 1. 5]?

Q: suppose A is a positive real number, determine the area of the traingle enclosed by the lines x=0,…

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Q: If a and b are integers, then a/b is always a rational number. True False

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Q: What number a>0 makes it that the area under the function f(x)=sin(2x) between x=0 and x=a is 1

A: The area under f(x) and between x=0 and x=a is given by: Given that this equals 1.  We have to…

Q: c) Estimate the area under the graph of f(x) = sin x from x = 0 to x = using four approximating…

A: Given function is fx = sinx x∈0,  π2 number of rectangles = 4 Step size  h= π2 -04   = π8 ⇒ h = π8…

Q: 3) Use approximating rectangles to approximate the area under the curve y = 4 – x2 on the interval…

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Q: 2

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Q: Find the mean, mode and median for the distribution df == 1 sin x dx, 0<xST. 2 ||

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Q: The Area between k*x3 and k*sin (x) is 2. What is the value of k?

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Q: Q1/ a) Sketch the graph of y = sin2x for 0 <x SI %3D b) find the total area bounded by the curve and…

A: This is a problem related to calculating area under curve of the polar equation. Based on the…

Q: How to find the median with an integral when f(x)=4(1-2x) on the interval [0,1/2]

A: Consider that a continuous random variable X has a probability density function f(x), over the…

Q: What is the area under the curve for f(x) = 3x2 +5 between x=1 and x=10?

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Q: (c) curve y = 5-x", line y=x+3 (d) y= sinx, y=cosx, x= 7 /4, x=7/2

A: Double integers

Q: Consider a function f continuous and differentiable on R with f(2. 5) = -3. 1 and f'(2. 5)=-0. 2.…

A: We have to find

Q: Find the area between f(x) = x and g(x) = (x-2)2 %3D

A: The given two curves are fx=x  and  gx=x-22. Evaluate the intersection points of the two curves as…

Q: C) Determine the area of the shaded region about the x-axis.

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Q: The graphing calculator gives the area bounded by the curve of y = ln x, the x-axis and the lines x…

A: Step 1: Given : Value obtained from graphing calculator  ∫14​ln(x)dx=2.5452 Step 2: The composite…

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 selection of the best element for a given system.

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, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

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 that have length, breadth, and height (or depth).

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.