1. The region of integration for f(x, y, z) dz dx dy is shown.. Write the integral in the five other orders. 212-y 0 JO 22-1-27 0 f(x,y,z)dxdzd plore behind XO 42Y Z-2-y y 2- Plane behind is yO f(yyz)dxdydz or x-1-29 or y=2- T. 1 2

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: 2. Give iterated integrals for (xz*)dS where S is the part of the cylinder x² + y = 9 above the…

A: Given that x2+y2=9 and the part of the cylinder which is above XY plane implying that z > 0. We…

Q: ex O (y +e*ln y)dx+ () dy be the line integral on the boundary of the region enclosed by Let y=3-x²,…

A: We need to find the equivalent double integral for the given line integral The given line integral…

Q: 7. Consider the iterated integral / T * dy dz. ly=z/2 (a) Explain why we cannot antidifferentiate e…

A: Given double integral is ∫x=0x=4∫y=x2y=2ey2dydx.

Q: Calculate the double integral √ √(8x + 2y + 16) dA where R is the region: 0 ≤ x ≤ 1,0 ≤ y ≤ 4.

A: The objective is to evaluate the double integral.

Q: Sketch the region R whose area is given by the iterated integral. *16 – y² dx dy 14 12 10- y 8. 4 2-…

A: Solve by using graph

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 that f(x, y) = yVa +1 at which {(x, y) | 0 < y < a < 4}. Then the double integral of f(c, y)…

A: Given that f(x,y)=yx3+1 The limit of the function are x limit:0≤y≤4y limit:y≤x≤4

Q: Which of the below double integrals has the following region? -2 I 1 1 1 1 T -1 4 2 0 -1- Select…

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Q: Choose five other iterated integrals that are equal to the given iterated integral. f(x, y, z) dz dy…

A: Given iterated integral,

Q: 2) Calculate the integral the regions descri bed. over / 2x- 5xy- 3y² dA. On a y = (x-1) /3 , y= -2x…

A: Bounding lines y=x3         → 3y-x=0y=(x-1)3→3y-x =-1y=-2x    →y+2x=0y=1-2x  →y+2x=1

Q: Which of the following properties is not applicable to double integrals: L° L* f (x, y) dydx and 2*…

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Q: 22. Here is the region of integration of the integral ILS c. dx dy dz e. dz dx dy. (0, -1, 1) (1,-1,…

A: Given data:- Region of integration of the integral ∫01∫-10∫0y2dzdxdy

Q: Suppose that f(x, y) and the region D is given by {(r, y) | 1 < # < 2,1 < y < 4}. D Then the double…

A: ∫∫D f(x,y) dx dy = ∫y1y2∫x1x2 f(x,y) dx dy

Q: (a) Compute the multiple integrals of (i) V4-z2 1 xy dxdydz (11) SS, (8 – x² – y²)dA, where R = {(x,…

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Q: 1. Give iterated integrals for r (x² + yz)dV where E is in the first octant bounded by the planes: y…

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Q: Given the domain 9 = {(1, y) | − 4 ≤ x ≤ 4, - 4 ≤ y ≤ 4}:: D the double integral of f(x, y) = 1 over…

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Q: Evaluate the double integral. (2x + y) dA, D = {(x, y) | 1 <ys 2, y – 1 < x< 1}

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Q: Evaluate the triple integral. y dv, where E = {(x, y, z) | 0 s x < 5, 0 s y s x, x - y szs x + y}

A: ∬∫EydV

Q: Suppose that f(æ, y) = yVæ³ + 1 on the domain D = {(x, y) | 0 < y < x < 1 D Then the double integral…

A: Given,

Q: 1. Evaluate the double integral r²y dA, where D is the region enclosed by the x-axis and the…

A: We can evaluate the double integral.

Q: Suppose that f(x, y) = 2x + 3y and the region D is given by {(x, y) | −1≤ x ≤ 5, − 1 ≤ y ≤ 5}. D…

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Q: 4. the value of the given integrals | z - i | = 2,(z € C) around the circle compute for positive…

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Q: Evaluate the triple integral. 2xy dV, where E lies under the plane z = 1 + x + y and above the…

A: Final answer is 65/84.

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: 22. Here is the region of integration of the integral dz dx dy 1J0 (0, – 1, 1) (1, – 1, 1) z = y²…

A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

Q: Consider the integral 3/2 1 I = Q dz dy + Q dz dy, which splits a region into two parts (because the…

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Q: Calculate the double integral over R = {(x, y) | 0<x< 3, 0sy s 1}. SS 4+4x2 R 1+y2

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Q: Verify Green's Theorem by evaluating both integrals (ON-OM) d [[ y² dx + x² dy = √ √ ( ³x for the…

A: In this question, we want to verify the green's Theorem for the given integral.

Q: 25. Evaluate the integrals. (a) |(*+y) d4, D bounded y =Vx and y= x. (b) [[[yz cos(x' HV where E =…

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Q: 1 Which one of the following integrals reverses the order of integration f(x, y)dydx? а. 2y 2-2y…

A: It is given that the double integration is ∫01∫y=x2y=1-x2 fx, ydydx. We have to write the double…

Q: #2. Evaluate the double integrals (a) || xyVx² + y² dA, R where R= {(x,y):0<x< 1, 0< y< 1}. (b) |…

A: We have to find the integral for given question       According to our guidelines, we can solve only…

Q: 3 The integral ³³ g(x, y) dxdy is equivalent 3 to ₁ ³x g(x, y) dydx

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Q: 3. Evaluate the triple integral where E is the region behind y = 10 – 2z and in front of the region…

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Q: Set up the definite integral that gives the area of the region. Yı = (x – 7)3 Y2 = x – 7 dx J6 y 1.5…

A: Given problem:- Set up the definite integral that gives the area of the region. Y1 = (x-7)³ Y2 = x -…

Q: Suppose that f(x, y) = 8x + 4y and the region D is given by {(x, y) | –1< x < 1, – 1 <y< 1}. D Then…

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Q: Consider the following line integral: $(a + sin(x*))ax + (2x²y-In(tan(/y)))dy where C is the…

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Q: Evaluate the double integral 4 = SS R y2 dædy over the region R={(x,y)|0 < x < 4, 1 < y < 4 }

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Q: 1- f(x, y)dydx? Which one of the following integrals reverses the order of integration a. 2y 2-2y…

A: We have to solve given problem:

Q: 4. Evaluate the double integral x cos y dA; R is the triangular region bounded by the lines y = x, y…

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Q: 3. Use the change of variables: u = x + y , v = y – 2x to evaluate the integral: Cx+y(y-2x)²dydx .…

A: Given: The change of variables: u=x+y and v=y-2x We have to evaluate the integral: ∫01∫01-xx+y y-2x2…

Q: Here is the region of integration of the integral dz dy dx. Тор: у +z%3D1 Side: y = x² (-1, 1, 0)…

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Q: Evaluate the double integral. 7x cos(y) dA, D is bounded by y = 0, y = x2, x = 7 %3D

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Q: The double integral ſſ 2xy³dA over the rectangular region R = {(x, y) E R“, 0< xS 4 and – 1< y< 0}is…

A: Dr

Q: Suppose that f(x, y) and the region D is given by {(x, y) |1< x < 2, 2 < y < 4}. Then the double…

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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: 3. Write five other iterated integrals that are equal to the given iterated integral 1 1-y S. SS.…

A: The given integral is                              ∫01∫x1∫01-yfx,y,z dz dy dx. To find: the order of…

Q: Suppose that f (x, y) = 8x + 7y at which {(x, y) | – 2 < x < 3, – 2 < y < 3}. - D Then the double…

A: Use the integrating limit given on the set separately for x aand y

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: 8) consider the region R in the first quadrant(xz0, y2) bounded by x=2y² X=Y²+1 a) set up, but clo…

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