Suppose your daily revenue from selling used DVDS is R(t) = 100 + 10t (0 < t< 5) dollars per day, where t represents days from the beginning of the week, while your daily costs are C(t) = 68 + 5t (0

Q: Use the Midpoint Rule with  n = 4  to approximate the area of the region bounded by the graph of…

A: Given:    Approximate using mid point rule:∫04x2+4x dx ,  n=4

Q: Find the area of the region between the graphs of y = 20 - 2² and y=-2x - 15 over the interval 6 < x…

A: Please see the below picture for detailed solution.

Q: Use a finite approximation to estimate the area between the x-axis and the graph of f(x)=2x^5…

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Q: Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of the…

A: We have to use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the…

Q: Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of the…

A:

Q: (a) Estimate the area under the graph of  f(x) = 4 + 4x2 from x = −1 to x = 2 using three…

A: In this Question I we taking the endpoint mid point and finding values

Q: Consider the function f (x) = –x² +9. What is the approximation of the net area under the curve of f…

A:

Q: Calculate the area, in square units, bounded above by f(x)=x2+4x+4 and g(x)=−4x+4 and bounded below…

A: Consider the curves, fx=x2+4x+4,   gx=-4x+4 To sketch the graph: Here there are two region be…

Q: Estimate the area under the graph 1 of f(x) = from a = 5 to x2 +1 b = 13 by using n = 4 rectangles…

A: The given function,   f(x)=11+x2 from a=5 to b=13 by using n=4 rectangles

Q: Find the area between the graph of y = x - 6x + 8 and the x-axis from x = 1 to x = 3.

A:

Q: Find the total area between the graph of f(x)=x2−5 and the​ x-axis from x=0 to x=6.

A:

Q: Consider the function f(x) = x² - 3x + 2 on [0,4], Find the total area between the curve and the…

A:

Q: Find the total area between the graph of the function f(x) = x + 1, graphed below, and the x-axis…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Estimate the area between the x-axis and the graph of f(x)=9−x2f(x)=9-x2 over the interval…

A: We will use rectangle's formula to evaluate the area of curve

Q: Find the area bounded by the parabolas (x-3)² - 16ky = 0 and y² - 16k (x-3) = 0.

A:

Q: Find the geometric area of the region bounded between the graphs of f (x), g(x) as given: f(x) = x2…

A: Sketch the graphs as shown below.

Q: Find the total area bounded by the x-axis and the curve f(x) = x2 + 3x - 4 over the interval [0, 4]…

A: The given curve is,

Q: Find the area of the region between the graphs of f(x) = 3x + 8 and g(x) = x2 +2x +2 over [0, 2]…

A: according to graph area of shaded region can be written as given below A=∫02fx-gxdx

Q: For the area under the curve f(x) = x(x+1)(x+7) above the x-axis, and between the vertical lines…

A:

Q: (a) Estimate the area under the graph of f(x) = 2 + 4x from x = -1 to x = 2 using three rectangles…

A:

Q: c) [ 1: Estimate the area under the graph of f(x) = x² - 1 from x = 1 to x = 3 using four…

A:

Q: Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of the…

A:

Q: Find the area between the y-axis and the graph X = 127 124 y² 2 1 -3 -2 -1 2 о T 4 3 0 -1 -2 1 on…

A: Given y-axis and x=1y2 on the interval -1,-3

Q: Find the area bounded by the two curves f(x) = x² – 8x + 8 and g(x) = - 2² + 6x – 8, and the two…

A: To find Area between two curves:  f(x)=x2-8x+8 and g(x)=-x2+6x-8 and two vertical lines x=3 and x=4.…

Q: Find the area bounded by the line f(x) = 3x – 5, the curve g(x) = x² – 10x + 7, and the two vertical…

A: Area between two curves :   If f(x) and g(x) be the two continuous function on a,b and f(x) ≥g(x) on…

Q: 2 Find the area of a triangle bounded by the y axis, the line f(x) = 8 – -x, and the line…

A:

Q: Find the total area between the curve of the function f(x)=2x+4 and the x-axis over the interval…

A: We have to find the total area under f(x)=2x+4 and the x-axis over the interval [−9,−1]Recall that…

Q: a) Estimate the area under the graph of f(x)=2x+1 from x= 1 to x=2 using four approximating…

A: Given problems:- a).  Estimate the area  under the graph f(x) =2x+1 from x=1 to x=2 using four…

Q: If R is the region between the graphs of the functions f(x) = 4x + 9x2 + 7x – 3 and g(x) over the…

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Q: Use the Midpoint Rule with n 4 to approximate the area of the region bounded by the graph of the…

A:

Q: Find the area of the region enclosed by the curves f(x) = 7x + 1 and g(x) = 5x + 17, and the lines x…

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Q: Find the area bounded by the curve 4y^2 +16x -15=0 and the line x=-1.

A:

Q: find the area between f(x)=x^2-16 and the x axis from x=0 to x-=9

A: The given function is fx=x2-16 We have to find the area between fx and the x-axis from x=0 to x=9

Q: Find the total area between the graph of the function f(x) = x + 1, graphed below, and the x-axis…

A:

Q: Find the area of the region between two curves f(x) = 3x + 1 and g(x) = x from x = 0 to x = 1.

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Estimate the area between the x-axis and the graph of f(x) = 9 – 2° over the interval [0, 3] by…

A: Given function is f(x)=9-x2 we have to find the area over interval [0, 3]. Since there is 3…

Q: Find the area between the curves f(x) = x2+2x+1 and g(x) = x+1

A: We need to find area between given curves.

Q: For F(x)= 3+3x-2x^2 A. Sketch the graph and the rectangles from x=0 to x=2 using n=4 and right…

A: The given function is:…

Q: Find the total area between the curve of the function f(x)=−2x and the x-axis over the interval…

A:

Q: Find the area bounded by the two curves f(x) = x2 – 8x + 8 and g(x) = - x² + 6x – 8, and the two…

A: The given two curves:fx=x2-8x+8 and gx=-x2+6x-8and the two vertical lines are x=3 and x=4.We need to…

Q: The area of the region bounded by the curves f(x)=x²+1 and g(x)=2x+1 is best described by: a. ² [(2x…

A:

Q: The area under the curve y = 7x bounded by the lines x = 4 and x = 8 above the x – axis is O 336.00…

A:

Q: 4. Find the surface area of the function x when revolved around the x-axis. between x=0 and x1

A: When a curve is revolved about an axis, we obtain a surface and there are several pre-defined…

Q: Consider the region bounded by f(x)=−x2+11x−3 and g(x)=5x+5. Find the area, in square units, between…

A: Given:

Q: Suppose your daily revenue from selling used DVDs is R(t) = 100 + 10t   (0 ≤ t ≤ 5) dollars per…

A: We need to find area between R(t) and C(t) for 0 ≤ t ≤ 5.

Q: Find the area of the region bounded by the curve y = x³ – 2x² – x + 2 and the x-axis for -1 <x<2, as…

A: We will solve this question by using double integration. where,  y=0 and y=x3-2x2-x+2 and x lies…

Q: Find the area between the curves f(x) = x^2 - 4x +12 and g(x) = x^2 - 2x + 2  for 0 ≤ x ≤ 3

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Q: Find the area between the curve y = x = 0 and x = 5. x(x 3) and the ordinates - LA B 3

A:

Q: Estimate the area between the x-axis and the graph of f(x) = 9 – x over the interval 0, 3 by using…

A: The given function f(x)=9-x2 over the interval [0,3]

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.