By making an appropriate change of variables, evaluate the double integral I = (z + y) e v drdy where R is the rectangle enclosed by the lines z - y= 0, z - y = 9, I +y = 0, and z +y= In (91) /9. Then what is I + In (91) /18 Answer:

Q: Evaluate the integral, where E is enclosed by the paraboloid z = 9 + x² + y?, the cylinder x2 + y2 =…

A: In cylindrical coordinates:-x=r cos θy=r sin θ z=z Also, x2 +y2 =r2  And, ∫∫∫f(x, y, z)…

Q: By making an appropriate change of variables, evaluate the double integral I = (z + y)e= v° dzdy…

A: By making an appropriate change of variables, evaluate the double integralI=∬R(x+y)ex2−y2dxdywhere R…

Q: Evaluate the given integral by making an appropriate change of variables. √√₁ 3 x - 8y dA, where R…

A: The objective is to evaluate the integral ∫∫R3x-8y3x-ydA, where R is the parallelogram bounded by…

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: Evaluate the given integral by making an appropriate change of variables. 9X - 3y бх — у dA, where R…

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Q: 3. Compute , xe*ydA where R is the rectangle 0 <x< 1,1< y< 2, using iterated integrals in both…

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

A: In this question, we have to evaluate the double integral by changing the variable for a given…

Q: Evaluate the Integral dz 1. S z²+4z ANSWER: 1. - In + C 4 |z+4

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Q: Set up an integral for the length of y = Vx + 2, 2<x<7 using ds : |1+ () dx. %3D A. ds = S, 1+ 1 dx…

A: Solution:Given        y=x+2    2≤x≤7using ds=1+dydx2dxFormula:ddxxn=nxn-1

Q: 2 4-2y 4x-x dxdy r2y 4x-x dxdy + e e

A: The reverse Order integration is:-

Q: (a) The Composite Trapezoidal Rule applied to the integral - [ f(z)dx I = gives the error b - a, 4h³…

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Q: Evaluate the double integral. 4y dA, D = {(x, y) | 0 s x s 1, 0 sysx} 6x + 1

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Q: Suppose that f(z, y) = /4 – a² – y² at which {(r, y) | 2² + y² < 4}. Then the double integral of…

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

A: Double integration

Q: Evaluate the double integral. 7y2 dA, D = {(x, y) I –1<y<1, -y – 2< x< y}

A: Explanation of the answer is as follows

Q: Calculate the double integral of f(x, y) over the triangle indicated in the following figure: y 3…

A: NOTE:- Due to the unavailability of a computer algebra system, the first question can't be solved as…

Q: Suppose that (x, y) = x+ 4y on the domain D = {(r, y) | 15x< 2, x? sys4. D Then the double integral…

A: Given that, f(x, y) = x + 4y and   {1≤x≤2},  {x2 ≤y≤4} We have to calculate the value of ∬Df(x, y)…

Q: Evaluate the given integral by making an appropriate change of variables. х - бу dA, where R is the…

A: The objective is to evaluate the integral: ∫∫Rx-6y3x-ydA, where R is the parallelogram enclosed by…

Q: Calculate the double integral of f(x, y) over the triangle indicated in the following figure: 4 3…

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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: *0 = x = 0, y = 1, x = y about the line y = 1 can be computed using the method of disks or washers…

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Q: The double integral T f(x)g(y)dydx,where a,b.c, and d are constants, is equal to

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Q: Evaluate the triple integral z dV, where is E bounded by the paraboloid x= 4y+4z2 and the plane x =…

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Q: Evaluate the integral, z' dv where, E lies between spheres2+y += 2 and +y += 3, for z 2 0

A: According to question,E lies between spheres,x2 + y2 + z2 = 2,andx2 + y2 + z2 = 3,x≥0

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

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Q: Evaluate the double integral. (2x + y) dA, D = {(x, y) | 1 s y s 2, y – 1sx s 1} 328 3.

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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: Evaluate the triple integral z dV, where is E bounded by the paraboloid x= 4y+4z2 and the plane x=…

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Q: Use the indicated change of variables to evaluate the double integral. 56xy dA x = 1/2 (u + v) y =…

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Q: Evaluate the triple integral 2xe" sin z dV, where Q is the rectangle defined by Q = [(x, y, z)| 0…

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Q: Evaluate the integral starting from C of ydx + xdy+ zdz, where C is given by x=cost, y=sint, z=t^2 ,…

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

A: Let us consider a triple integral  Then there are 6 different ways to write the iterated triple…

Q: Evaluate the double integral. 4y Vx² - y? dA, D - {tx, v) I 0 s x s 3, 0 sysx}

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Q: Evaluate the line integral, where C is the giv z² dx + x² dy + y² dz, C is the C

A: See the details solution in below

Q: Evaluate the double integral [[ cos(x + y) dA, where R is the region bounded by the lines y = r and…

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Q: Evaluate the triple integral. SS. dV x² + z? E = {(x, y, z)| 1 <y< 4, y<z< 4, 0<x< z

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Q: Use an appropriate change of variable to evaluate the double integral: y- x cos y +x d A, R where R…

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Q: Evaluate the line integral of f(x,y) along the curve C. f(x,y)=x +y, C. y= - 2x + 4, 0<x<3 O A. 21 О…

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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 line integral. L(4x – 8y) ds C:x + y = 100 (4x - 8y) ds = i |

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Q: dV, where E is the region between two cylinders ²+², 5. Evaluate the integral and 2² +2²9 with 1 ≤ y…

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Q: se the fact that 1 dr %3D 2e2 Ae 2r +C p either evaluate the improper integral -d.r, or show that it…

A: we have to find integration.

Q: Evaluate the given integral by making an appropriate change of variables. 2 = BY dA, where R is the…

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Q: Calculate the double integral of f(r, y) over the triangle indicated in the following figure: 4 3…

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Q: Evaluate the given integral by making an appropriate change of variables. 10 X - 4y dA, where R is…

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Q: x = 0, y = 1, X = %3D about the line y = 1 can be computed using the method of disks or washers via…

A: According to the problem, we have

Q: Evaluate the triple integral. {x, y, z) | 0 s y s 2, 0 sxs 4- y², 0 sz s Sy 6x dV, where E =

A: From the given problem:   ∫∫∫E6xdV   And region:   0≤y≤20≤x≤4-y20≤z≤5y   So, we can write as:…

Q: The double integral f(x)g(y)dydx ,where a,b.c, and C d are constants, is equal to

A: