4. Consider the figure below with the indicated regions bounded by the graph of f(r) and the -axis. Find the area of each region by using geometry and use this information to evaluate the definite integrals given below. f(x) 4 R3 R1 3 2 3 -5 -4 R2 1 -3 -4 -5 Area of R3 Area of Ri Area of R2 f) dr f(z) dr

Q: Suppose y = f(x) = 5x – x². A graph for this function and area is given below. 23. Shade in the…

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Q: Set up the definite integral required to find the area of the region between the graph of y=x2-17…

A: First draw the curves and find their intersection  points then use integration to get the area.

Q: Show that the area between the curve y = 1/x and the x-axisfrom x = 10 to x = 20 is the same as the…

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Q: 1. Find the area in the first quadrant bounded by f(x)=4x-x^2 and the x-axis. f(x) = 4x-x² 3 2 3 1 2…

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Q: Suppose the region on the left in the figure (with blue shading) has area is 24, and the region on…

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Q: Find the area under the graph of y = -x² AL 54 3-2 -11° 1 2 3 4 5 X 4x on the interval [-4, -2].

A: We will solve the required.

Q: Evaluate the integrals of the functions graphed by using the formulas for areas of triangles and…

A: NOTE: Refresh your page if you can't see any equations. . the height of the small triangle is h=1…

Q: Evaluate the integrals of the functions graphed by using the formulas for areas of triangles and…

A: Area of the Triangle = 12×base×height Area of Circle = πr2

Q: 5. Find the area bounded by the curves y = x4 – 4x2 + 4 and y = x2. -2

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Q: Find the area of the region bounded between the curves y = sin(x), y = cos(x) on the following 4 -27…

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Q: 6. Find the area between the curve y = x(x - 3) and the ordinates x = 0 andx = 5.

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Q: Suppose we want to know the area of a region that is bounded by the graph of F(X)=1/2x+2 and the…

A: Consider the given curves.

Q: Write a definite integral that represents the area of the region. y1 = x2 − 4x + 3 y2 = −x2 + 2x + 3

A: Where, From the graph we can see that the points of intersection of these two curves are,

Q: 2. Find the area enclosed by the curve y2 = x6 (1- x²)³.

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Q: Evaluate the integrals of the functions graphed by using the formulas for areas of triangles and…

A: To evaluate the integrals using the formulas for area of triangle and circles.

Q: Evaluate the integrals of the functions graphed using the formulas for areas of triangles and…

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Q: In the figure, the regions A, B, C and D bounded by the x-axis and the graph of f have the following…

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Q: The graph shown below is fx) = (x - 2)2. What is the integral function g(x) that defines the area…

A: Given: f(x) = (x - 2)2 What is the integral function g(x) that defines the area under this line…

Q: 5. Recall that the length of the curve represented by a function y= fa) on an interval (a, b] is…

A: Since multiple questions are posted the first question is answered as per our guidelines.Kindly…

Q: 3. Find the area bounded by the curve ay2 = r and the line x= 4 a. Ans. 142 a=

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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: The graph shown is f(x) = x³ + 2. 5 4 3-21 1 2 3 4 5 What is the integral function that defines the…

A: The answer is in step 2.

Q: 2. ) Find the area below f cx) -x +7x*- 1o x +3 over the interval 1L x<2 (Drow and Illustrate the…

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Q: 3) Find the area bounded by the curves: x² – 4x + 1 = 3y and x2 + 2x + 2y – 5 = 0.

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Q: 11. Set up and evaluate integral to find the area of the region bounded between the x-axis and the…

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Q: 1. Set up the integral(s) to find the area of the region bounded by y = -x² + 2x +5 and y = x3 - 3x2…

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Q: The accompanying figure shows four regions bounded by the graph of y = x sin x: R1, R2, R3, and R4,…

A: Given  The four regions bounded by the graph ofy = x sin x . R1, R2, R3, and R4, whose areas are 1,…

Q: 4. Consider the region R bounded by the parabolas y = įr² and y = r² – 3r, as depicted in the graph…

A: I use washer method to find volume about line y=-5

Q: Below is the graph of y = x² +5. 141 12- 10 -2 -1 8- 6- 4- 2 0 1 2 3 The area bounded by y = x² +5…

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Q: 3. Find the area bounded by the graph of the indicated equations over the given intervals (when…

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Q: What is the area bound between the curve y= \x/2 and the x-axis between x =-3 and 4/2 - 2/3 3 x = 2?…

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Q: 1. Find the area of the region bounded by f(x) = x, the x-axis, and the vertical lines x = 0 and x…

A: Given: 1.f(x)=x3  x=0 and x=1

Q: 1) Find the area of the region bounded by the curve y=3x•e-2* and the x-axis, for x>0. i) Rou imal

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Q: 1. Find the area bounded by the curve y = x^2, the x- axis, and the ordinates x = 1 and x = 3.

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Q: 1. Find the area of the region bounded by the given curves. a) y = 2x° - x² - 5x + 4, y= - x² +3x…

A: We have to find the bounded area by curves

Q: 1 75. Find the area of the region bounded by the curve f(x) = (16 + x²)-3/2 and the x-axis on the…

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Q: In the figure, the regions A, B, C and D bounded by the x-axis and the graph of f have the following…

A: Here we will find the definite integral,

Q: Approximate the area under the curve of y =-+x+5 over the interval x = -1 to x = 4 using 5 left…

A: Formula: Using left end points AL = Δx[f(xo)+f(x1)+......+f(xn-1)

Q: 5. Use the concept of the definite integral to find the area of the region under the graph of y =…

A: we have to use the concept of the definite integral to find the area of the region under the graph…

Q: 1. Determine the area of f (x) = 3 + 2x – x² and above the x axis. - X - 3x 3 3 2. Determine the…

A: To find the area of f(x) and above the x-axis, use the formula, A=∫-13f(x)dx and substitute f(x)…

Q: 5) The following diagram shows the graph of f(x): for x +1 0<x<4, and the line x = 4 Let "R" be the…

A: Area under the curve from 0 to 4 is

Q: 48. Evaluate the integral ,(x² + y²)-² dA, where R is the region inside the circle x² + y² = 2 for x…

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Q: 3. Find the area bounded by the curve y = x² - 7x + 6 and the x-axis and the ordinates x 2 and x =…

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Q: Evaluate the integrals of the functions graphed by using the formulas for areas of triangles and…

A: Lets calculate the area of the two triangles above the x-axis. The first triangle is from x = 0 to x…

Q: 3. Find the area bounded by the curve y = - x² x = 1, and the x-axis. %3D x4 – 16

A: We first sketch the region using a graphing calculator.

Q: 1. Which of the following definite integrals could be used to calculate the total area bounded by…

A: This question is related to definite integration, we will solve it using given information.

Q: Approximate the area under the curve of y = x - 2x + 3 over the interval x=-1 to x = 3 using 4 right…

A: Find out the area under the curve using 4 right endpoint rectangles.

Q: 1) The region R in the first quadrant is bounded from above by y = 2x+9 and below by y = x² +3. Find…

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Q: (0,3) 1 (-3,0), (3,0) -2 -1 -1 (0,+V3)

A: We will solve the following