B is the region bounded by the following graphs: 1 A1:]y – 1| =;x 2 Аz: (у — 4)2 %3D -4 (х — 6) Using vertical triangles, set up the sum of definite integrals equal to the area of region B. Show both the non-simplified and simplified/final answer.

Q: Set up the definite integral that gives the area of the region. Y1 = (x – 7)3 Y2 = x – 7 %3D dx 196…

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Q: Given a region R enclosed by the curves: (x-2)² y = 1 + sin() , y = y = 4_ @a and x = 2 as shown…

A: The region R is enclosed by the below curves. y=1+sinπx4y=4−x−224x=2 To set up a definite integral…

Q: B is the region bounded by the following graphs: 1 A1: ]y – 1| = ;x A2: (y – 4)² = –4(x – 6) %3D…

A: According to the question,Given curve,A1 : y-1 = 12x,A2 : y-42 = -4x-6

Q: verify Green's Theorem by evaluating both integrals * dx + x*dy = aM dA for the given path.

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Q: Find the value of k such that the area of the region under the curve y = x(k – x), (0 < x < k), is 1…

A: Given: To find the value of k such that the area of the region under the curve y=x(k-x), (0≤x≤k) is…

Q: Evaluate the following integral: b.) !!!! xyz dv if S is the region bounded by the cylinders ² + y²…

A: According tot the given conditions the limi values of x,y and z are0≤x≤50≤y≤25-x20≤z≤25-x2Hence…

Q: Suppose D is the region bounded between the z-axis, the curve y = e", and 0 <I<1. Compute the…

A: We need to compute the integral: ∫∫D2ydA Given that, y=ex and 0≤x≤1.

Q: Set up the definite integral required to find the area of the region between the graph of y = 14-2²…

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Q: 2/ Find the area of the region enclosed by the curves y=lx) and 0on the interven-4] A3 B. D, IS

A: Given: Area enclosed by y=|x| and y=0 on the interval [-1,4]

Q: 2. Consider the region bounded by the graphs of y = 3* – 1 and x = y² – 3, illustrated at the right.…

A: The objective is to setup the integral that calculate the center of mass of the region bounded by…

Q: Let M]M be the region in the first quadrant bounded by the graphs of y=sin(πx2)y=sin(πx2) and…

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Q: Area = 2c 27 dx

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Q: b. Set up the definite integral that gives the area of the region inside the limaçon but outside the…

A: The area between any 2 polar curves is given by the formula   where r is the polar curve and is the…

Q: Sketch the region enclosed by y=e^3x ,y=e^8x, and x=1. Decide whether to integrate with respect to x…

A: The given two curves and horizontal line

Q: 2 Evaluate 2 dA where D is the region described by 0s ys 55 - x Integral is equal to : Enter an…

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Q: Set up the integral to find the area of the region bounded by y x2-1 and y = r+ 5

A: topic- area bounded by curves

Q: Set up the definite integral required to find the area of the region between the graph of y = 11 – x…

A: Upon plotting both the graphs y=11-x2 and y=-3x-43 we get Here red curve is y=11-x2 and blue one is…

Q: 1. Evaluate the integral and sketch the region of integration fo S e-rro drd0

A: Definition used -              Double integral with polar coordinate -…

Q: Sketch the region R whose area is given by the iterated integral. 16 – y2 dx dy 3 2- 2 6 8. 10 12 14…

A: option B

Q: Set up an integral representing the area A of the region enclosed by the given curves. x = y4, x = 2…

A: given,

Q: 1. In each part, use a definite integral to find the area of the region, and check your answer using…

A: 1. Area of the region is given by the definite integral ∫022−xdx∫022−xdx=2x−x2202…

Q: The region D is bounded by the curves y = 5, and y = 5x². Which of the following can be used to…

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Q: 1. Sketch the region and evaluate the following integral |1. (VI++1)dydx 72 y 4 2 ++++++++H 3 -1 1 4…

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Q: Sketch the region whose area is given by the definite integral. 36 - x2 dx y y 12 35 30 25 20 15 10…

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Q: Which one of the following integrals represents the area of the region enclosed by the two curves y…

A: If two function y=f(x) and y=g(x) continuous on [a,b] and f(x)≥ g(x) on a≤x≤b, then area of the…

Q: 2 In y 1) Sketch the region R and express |e* dxdy as an equivalent double integral with the order…

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Q: 1. Let A be the region enclosed by the curves y = r² + 1, y = (2x – 1)² and r = 1. 2 ty y = x² +1…

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Q: Evaluate the double integral 4.x dydr 9 + y2 I when A is the shaded region in enclosed by the graphs…

A: Evaluate the double integral.

Q: Verify Green's Theorem by evaluating both integrals aN y2 dx + x2 dy dA ду - əx for the given path.…

A: For c-1 sign is negative because of opposite direction

Q: Set up a definite integral to find the perimeter of the region bounded by y = ex, y = e-x, and x =…

A: Given curves are: y=ex;y=e-x The point of intersection of these curves is obtained when:…

Q: Verify Green's Theorem by evaluating both integrals ƏN dA əx ду for the given path. C: boundary of…

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Q: Identify the integral with Type I region between S 2ny dx dy and S 2ny dy dx g(y) g(x) and compute…

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Q: Draw the region whose area is given by the definite integral. Ay 40- Sa2-2 36 - 2x)dx 32- Use the…

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Q: 11. Use the Shell Method to calculate the volume V of the solid obtained by rotating the region…

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Q: Evaluate |// e-V where E is the region between two cylinders z + = 4 and r +=9 with 1< y55 and : <0…

A: We will find out the required value.

Q: 4. Evaluate the integral (a + y) dA; where D is the region bounded by y = and the line y = }- x.

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Q: Set up the integral to find the area of the region bounded by y = r² − 1 and y = x + 5.

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Q: Consider the area of the region bounded by the curves y = 2x +1;x+y=7 andx=8. Which of the following…

A: We need to find the expression for the moments in x.

Q: Set up a definite integral to find the perimeter of the region bounded by y = e^x, y = e^−x , and x…

A: From the given problem:   y1=ex,y2=e-x,x=1 To find the perimeter, we need to add the length of the…

Q: Use an iterated integral to find the area of the region bounded by the graphs of y = 6x ² and y = ²…

A: Topic = Area

Q: A region is bounded by the y=x² and y=6x-x2, Which of the following integrals would approximate the…

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Q: Consider the following integral. Sketch its region of integration in the xy-plane. 8xy dy dx 4-x²…

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Q: Set up the definite integral that gives the area of the region. Y1 = x2 + 2x + 4 Y2 = 2x + 8 dx -2

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Q: 1. Find the area of the finite region enclosed by у%3D — (х + 1)(х — 3) аnd y %3 0 | -

A: Given: y = -x+1x-3,  y = 0 To find: The area of the finite region enclosed by  y = -x+1x-3, y = 0.

Q: Verify Green's Theorem by evaluating both integrals ƏN [< y² dx + x² dy = √₂₁ / (™N - 3W) CIA dA əx…

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Q: Find the area of the region bounded by y=x2, y=1, and x=0 revolved around x=2 using both the shell…

A: Shell method: Let a cylindrical shell which is at distance x from the y-axis, having thickness dx,…

Q: Set up the definite integral that gives the area of the shaded region bounded by the graphs of y,…

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Q: Set up the definite integral that gives the area of the region. Y1 = x2 + 2x + 5 Y2 = 2x + 30 %3D…

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Q: Set up the definite integral required to find the area of the region between the graph of y 20-z and…

A: Set up the integral