10. Evaluate the given integral using a change of variables of your choice. Sketch the original region of integration, R, and the transformed region S. J, e*ydA, where R is the region bounded by the hyperbolas xy = 1 and xy = 4 and the lines 2= 1 and 2 = 3

Q: Evaluate the double integral [₁ Where D is the region delimited by the lines y = 0, y = x³, x=0, x=1…

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Q: Evaluate the integral| c. ff sin x dA; R is the region bounded by the lines y = 2x, y = x and x = .

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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: Verify Green's Theorem by evaluating both integrals dk + x° dy = /. / dA ду for the given path. C:…

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Q: 2. Evaluate the following integral where R is the region enclosed by the lines 2x + y = 0, 2x + y =…

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Q: Use an iterated integral to find the area of the region. dy dx = y 8 7 5 4 3 2 1 -1 1 4 -1l 3. 2.

A: We need to setup and evaluate 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: ON Verify Green's Theorem by evaluating both integrals 7y dx + 7x*dy = J J]a дм ƏA for the path ду…

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Q: Verify Green's Theorem by evaluating both integrals ƏN y² = / / dx + x2 dy dA - Əx ду for the given…

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Q: Evaluate the following integral using a change of variables. xy dA, where R is the region bounded by…

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Q: Evaluate the given integral over the given region. ∬R (x + xy)dxdy; R : 1 ≤ x ≤ 3; 0 ≤ y ≤ 4

A: Given, To evaluate ∬R (x + xy)dxdy; R : 1 ≤ x ≤ 3; 0 ≤ y ≤ 4

Q: [[(r + 2y) dA; R= {(r, y) : 0 s r s 3, 1 s ys 4}

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Q: 16. Use the indicated change of variables to evaluate the double integral y sin xy dA where R is the…

A: We have to evaluate    ∬Ry.sin xy dA Region Bounded by xy=1, xy=4, y=1 and y=4. We have to assume…

Q: area ZA (xy) dx dy y/3 10.

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Q: Verify Green's Theorem by evaluating both integrals ƏM ? dx + x² dy dA ax ду for the given path. C:…

A: Given : ∫c y2 dx + x2 dy , Where, c : boundary of the region lying between the graphs of y =x &…

Q: Verify Green's Theorem by evaluating both integrals aN dx + x² dy = / / dA ay y2 ax for the given…

A: To verify green's theorem by evaluating both the integrals.

Q: Evaluate the integral ∫∫D (2y − x)dA where D is the region bounded by y = x^2 and y = 2x.

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Q: Evaluate the integral. SSS_* √x² + z² av E where E is the region of integration bounded by the…

A: To solve this put x=rcos(theta) And z=rsin(theta)

Q: Use Green's Theorem to evaluate the line integral. dx + ху dy C: boundary of the region lying…

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Q: Verify Green's Theorem by evaluating both integrals dA dx + x2 dy ax for the given path. C: boundary…

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

A: given,

Q: Evaluate the double integral / |: xy dA where D is the region bounded by the line y = x – 1 and the…

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Q: Evaluate the following integral: where Q is the region limited by: Q ={F (x,Y, z): 2<x= 3,0 <y<1, -…

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Q: For the following integrals, draw a sketch of the region of integration. (a) (c) / / (r, y. =)…

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Q: Evaluate the triple integral. 3xy dV, where E lies under the plane z = 1 + x + y and above the…

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Q: 4. Compute the integral x sin (xy) dA where R is the region 0 <x <1 and 0<y < .

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Q: 3. Use a suitable change of coordinates to calculate the integral / x² – y² dA, where R is the R…

A: The region R is given by

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: 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: Use Green's Theorem to evaluate the line integral. for y2 dx + xy dy C: boundary of the region lying…

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Q: Evaluate the triple integral. SSSE 7xy dV¸ where E lies under the plane = 1+x+ y and above the…

A: We have to Evaluate the triple integral.

Q: Use Green's Theorem to evaluate the line integral of C to the function (y − x) dx + (2x − y) dy  for…

A: To evaluate: ∫Cy-xdx+2x-ydy using Green's theorem where C is the boundary of the region lying…

Q: Evaluate the double integral Jl, x dx dy where the region R is bounded by: 3 y = 4x – 3, y =x +, y =…

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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: 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: Verify Green's Theorem by evaluating both integrals | y² dx + x2 dy dA ax for the given path. C:…

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Q: Evaluate the integral by making an appropriate change of variables. 9 cos( 3 (Y-X)) dA where R is…

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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: 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: 2. Evaluate the following integrals. (c) SS, e**+y´dA, where R is the region bounded by the circles…

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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: [[ 6r"e="vdA; R = {(r, y) : 0 < r s 2, 0 s y s 2}.

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Q: Verify Green's Theorem by evaluating both integrals ƏN ƏM ² dx + x²c dA JR Əx ду for the given path.…

A: Given the integrals: ∫Cy2dx+x2dy=∫R∫∂N∂x-∂M∂ydA for the given path: C: boundary of the region…

Q: Use an iterated integral to find the area of the region. dy dx = y 81 7 5 4 3 2 1- 1 2 3 4 6 8

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Q: Evaluate the triple integral, (2x + z) dV where E is the region bounded inside the cylinder a – y"…

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Q: Evaluate the triple integral. 4xy dV, where E lies under the plane z = 1 + x + y and above the…

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Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

A: First I have changed the line integral into double integral with the help of Green's theorem and…

Q: 2. Evaluate the iterated integrals by (i) viewing R as a type I region, and/or (ii) viewing R as a…

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

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Q: (d) If R is the region bounded by y = x² and y = 2x² – 4, then | S(x, y) dA as R an iterated…

A: Given, y=x2y=2x2-4