By making an appropriate change of variables, evaluate the double integral = || (x + y)e²-y° dædy R where R is the rectangle enclosed by the lines x – y = 0, x – y = 3, x + y= 0, and = In(25)/3. x + y Then what is I+ In(25)/6 Answer:

Q: For the integral sin(x) -∞ x(x²–2x+2) dx, which one is correct ? O The contour integral is eiz dz…

A: Given integral is ∫-∞∞sin(x)x(x2-2x+2)dx Its contour integral will be ∮eizz(z2-2z+2)dz So option (1)…

Q: Consider the following double integral: /[x+ y+1)dr dy, I: where D is the rectangle D: 0<<1,0< y< 2.…

A: We have to evaluate the integral and show that I in [2,8].

Q: Use the indicated change of variables to evaluate the double integral 16(x2 + y²) dA 1(u +v) X = %3D…

A: We need to find the indicated change of variables to evaluate the double integral ∬R16x2+y2dA where…

Q: || x²v d4 where D { (x,y) : xs y s 2+x, -1sxs2}. 2. sys2+x,-1<x<2}. D

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Q: Calculate the following double integral a(x+y)dxdy-[ where 2 = {(x, y) :0sys 2x+2,0 <x<3} Submit the…

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Q: Evaluate the triple integral. y dV, where E = {(x, y, z) | 0 < x< 8,0 s y s x, x – yszsx + y}

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

A: Greens  theorem verification

Q: By making an appropriate change of variables, evaluate the double integral -y? (x+ y)e²²-v° dædy

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Q: Evaluate the integral by integrating with respect to​ x, y, and z.

A: Given integral is,

Q: Evaluate the triple integral. II y av, where E {(x, y, z) | 0 s x s 5, 0 s y s x, x - y szS x + y}

A: Here, we have to evaluate the triple integral

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: Q1. Evaluate the integral, xy dv ху dV E where, E lies between spheres x? + y? + z? = 1 and x? + y +…

A: According to question,Given E lies between spheres,x2 + y2 + z2 = 1,andx2 + y2 + z2 = 2,for z≤0,

Q: Evaluate the integral (x + z) dS where S is the part of the cylinder y + z2 = 4 with x E [0, 9].

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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 triple integral. y dV, where E = {(x, y, z) | 0 < x < 5, 0 < y s x, x – y < z s x + y}

A: To evaluate the given triple integral.

Q: Express the integral  ∭Ef (x, y, z)dV , as an iterated integral in six different ways, where E is…

A:

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

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

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Q: Evaluate the double integral. y dA, D = {(x, y) | 0 s x s 2, 0 sys Vx} x2 + 1

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Q: The double integral ff 2xycosydA over the rectangular region R = {(x, y) E R?, 0< x<1 and 0 <y<n}is…

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Q: Evaluate the triple integral. (x - y) dv, where E is enclosed by the surfaces z = x² - 1, z = 1 -…

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Q: 16x? +z? = 16. Write the integral of f(x,y,z) over D in the order given below. SSS xy2) dz dx dy D |…

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Q: Evaluate the double integral. y dA, x2 + 1 D = {(x, y) | 0 <x< 3, 0 sy s Vx} ID

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Q: evaluate the triple integral given by fff (x + 2y)dV, where E is bounded by the cylinder y = x² and…

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Q: Evaluate the integral [[[var !!! y² dv where G is the solid in the first octant that lies below the…

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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: Evaluate the triple integral. (x - y) dv, where E is enclosed by the surfaces z = x² - 1, z = 1 -…

A: First, draw the region E, bounded by z=x2−1,  z=1−x2,  y=0, and y=8. The region is bounded below by…

Q: Evaluate the following integrals. 1 (a) dz dy dx. e (b) TI Vx2 + y2 dV, where E is the solid in R3…

A: we have to find the integrals 1) ∫01∫01∫y1e-z2dzdydx 2) ∫∫∫Ex2+y2dV,where E is solid bounded…

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

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Q: The correct value of the double integral below is S Sp(2x +y)dædy, D={(x,y)|1 < y< 2, y – 1 < x <…

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Q: Which of the integrals below is equal III fx.y, z) dz dy dx? Explain. to (a) J.JJ f(x, y, z) dz dx…

A: Given  The integration is ∫13∫02∫-11f(x, y,z) dz dy dx .

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: Suppose that f(x, y) = /16 – a? – y? at which {(x, y) | a? + y? < 16}. %3D Then the double integral…

A: Evaluate the double integral using polar coordinates

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

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Q: Use the indicated change of variables to evaluate the double integral. 4(x2 + y²) dA X = y = (0, 1)…

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Q: Use the indicated change of variables to evaluate the double integral. 8(x + y)e* - Y dA x = u + v)…

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Q: The region under the curve y = x2 x between 1 and x 3 is revolved about the line x = 3. Using the…

A: When we revolve around the x = 3 axis, then then the radius of the shell will be: R = 3 - x, height…

Q: Suppose that f(x, y) = 4- a? - y? at which {(x, y) | a? + y? < 4}. tr=2 Then the double integral of…

A: Change it to polar coordinate.

Q: Express the given integral as an equivalent iterated integral in the new order dx dz dy. 10 V x-…

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Q: Evaluate the triple integral. III. 7z dv, where E is bounded by the cylinder y2 + z² = 9 and the…

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Q: ; Evaluate the triple integral Answer: II z dV, where E is bounded by the cylinder y² + z² = 9 and…

A: evaluate the triple integral ∫∫∫Ez dV where E is bounded by the cylinder y2+z2=9 and the planes x=0…

Q: 4. Compute cach of the following iterated integrals by reversing the order of integration. sin (r)…

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Q: 2. By finding an antiderivative, evaluate each of these integrals, where the path is any contour…

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Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) YV 6 +…

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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: Evaluate the triple integral. SI. {(x, v, z) | 0 < y s 2, 0 < x < V4 - y?, 0 < z < 5y} 2x dV, where…

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Q: To evaluate the integral xe2" da using integration by parts, the best choices for u and dv are: u =…

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Q: Evaluate the triple integral. SSLE2: dV, where E is bounded by the cylinder y? + :2 = 9 and the…

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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,…