Use the transformation u =x + 4y, v = y-x to evaluate the given integral by first writing it as an integral over a region G in the uv-plane. 3. 5 3-4y (x + 4y) e V – x) dx dy 3 5 3-4y (x + 4y) e - X) dx dy = y (Type an exact answer.)

Q: I need help with part b

A: Given transformation is,

Q: Let f(x, y) = e-(x+y) for x ≥ 0 and y ≥ 0. (a) Compute of f(x, y) dx dy (b) Compute the double…

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Q: - Consider the region R enclosed by the two curves: y = 2(x – 1)3 - I = (y/2)5 + 1 %3D (2, 2) R…

A: As per as our guidelines i am supposed to answer only three part of this question please re-post…

Q: · ] x = 1 dA over a square region Using the transformations u=x-y and v=x+y to evaluate Rx+y with…

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Q: Verify Green's Theorem by evaluating both integrals aM y? dx + x² dy = | / (G dA ay əx for the given…

A: Solved below.

Q: Evaluate the triple integral over the bounded region E of the form  E = {(x, y, z)| g1(y) ≤ x ≤…

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Q: Consider the following line integral. fwo dx + x2 dy, C is counterclockwise around the rectangle…

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

A: Here we have to verify the Green's theorem.

Q: Using the u = z , v= z– y, w = zx integral output transformation SS. So-a'x'dv Where D is the region…

A: To find the integral, ∫∫∫Dy-z3 xz3 dV where D is the region defined by the functions, z=1,  z=y-2,…

Q: Consider the following line integral. pxy dx + x? dy, C is counterclockwise around the rectangle…

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Q: a. Find the Jacobian of the transformation x=u, y = 3uv and sketch the region G: 1 sus2, 3s3uv s6,…

A: a) The Jacobian of the transformation of  x=u,y=3uv will be J=∂x∂u∂x∂v∂y∂u∂y∂v  =103v3u  =3u

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. O…

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Q: (i) Evaluate the double integral (x + y) dxdy where D is the triangular region in the xy plane with…

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Q: Evaluate the double integral f(r, 0) dA. (5 cos(e) r dr de Sketch the region R. n/2 A/2 3 4 1 3 -3…

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Q: Evaluate the double integral f(r, 0) dA. 3 cos(0) r dr de Sketch the region R. T/2 л/2 2 2 -1 1 -4…

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Q: et $ (y +e*ln_y) dx+ (- dy be the line integral on the boundary of the region enclosed by Let…

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Q: a dA over a square region Using the transformations umx-y and v=x+y to evaluate with vertices (0,2):…

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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: Evaluate the integral of the two-form w = 3xe 3zy d A dy over the region D= {(x, y) E R² | x € [1,…

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Q: Sketch the region R and evaluate the iterated integral f(x, у) dA. (1- 6x + 8y) dy dx y 2.0 3- 1.5…

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Q: Sketch the region R and evaluate the iterated integral F(x, y) dA. (1 - 2x + 8y) dy dx 2.0- 2.0 1.5…

A: A detailed solution is given below

Q: The double integral f 2xy dA over the rectangular region R = {(x,y) E R, 0<x<4 and– 1<y<0}is equal…

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Q: Set up, but do not evaluate, an iterated integral for , dv, where E lies under the plane = 4 + x + y…

A: Triple integral set-up

Q: Evaluate the double integral Sr S f(r,0) dA, and sketch the region R. 9– r² dr d0

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Q: 3.a) Given the double integral fS,(r-y)e-v° dxdy, where D = {(x, y) : 0 <x+y < 1 & 0<x-y< 2},…

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Q: Evaluate the double integral f(r, 0) dA. -7 cos(0) r dr de 497 2 Sketch the region R. 7/2 A/2 6 2 4…

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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: 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: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly.…

A: Here we have to use green's theorem.

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

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Q: Evaluate the integral, where E is enclosed by the paraboloid  z = 4 + x2 + y2,  the cylinder  x2 +…

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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: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. O 3…

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Q: Use the transformation u =x + 2y, v=y-x to evaluate the given integral by first writing it as an…

A: The answer is in below steps.

Q: 2. Evaluate the double integral over the rectangular region R. (a) ffx√1-x² d4; R={(x,y):0≤x≤1,…

A: dA is the small changes in area due to small change in lenght and breadth i.e dx and dy so dA can be…

Q: Use the transformation u = x+ 6y, v = y - x to evaluate the given integral by first writing it as an…

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Q: Evaluate the double integral I = I | (2 – cos(x – y)) dA - when D is the bounded region enclosed by…

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Q: Use Green's Theorem to evaluate the line integral. Begin by sketching the region S. (e* + 5y) dx +…

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Q: State the double integral f S (x2 – y?) dx dy where R is the region in bounded by |x| + ly| <9 with…

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Q: Use Green's theorem to evaluate the integral for S[(6y-e*) dx +(8x+ lIn(4y)) dy]. where C is the…

A: Evaluate the integral              ∫C6y-e3xdx+8x+ln(4y)dy using Green's theorem, where C is the…

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. $ 6…

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Q: The double integral ſſ 2xy³dA over the rectangular region R = {(x, y) E R², 0<x<4 and– 1<y<0}is…

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Q: Compute the integral of the function f(x, y) x2 + 3y2 in %3D polar coordinates on the region D =…

A: we have to find the following integral in polar coordinate region

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. p 2…

A: Given problem:-

Q: The double integral ff 2xy³dA over the rectangular region R = {(x, y) E R², 0<x<4 and–1<y<0}is equal…

A: Given that, I=∬2xy3dA and  0≤x ≤4  and  -1≤y≤0 here dA = dxdy

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: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 5…

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. O 4…

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Q: The figure shows the region of integration for the integral. * 16-x² [4-x f(x, y, z) dy dz dx…

A: Consider the given integral ∫04∫016-x2∫04-xf(x,y,z)dydzdx and  y(x)=4-xz(x)=16-x2

Q: Evaluate the triple integral. 5xy dV, where E lies under the plane z = 1 + x + y and above the…

A: Given that z=1+x+y The range of the variables are, 0≤x≤10≤≤x0≤z≤1+x+y Then, the integral is,…