Evaluate the triple integral (ry + z) dV where E is the rectangular box: 0 < I< 1, 0 < y < 1, and –1< z < 1.

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: Evaluate the iterated integral. 21 V441-y у dx dy 21 441-y у dx dy %3D i

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Q: Set up, but do not evaluate, an iterated integral for , dv, where E is a cylinder of radius 3 cut…

A: We will have to set up an iterated integral ∫∫∫EdV where the E is a cylinder of radius 3 cutoff on…

Q: Evaluate the triple integral of (1 − x2 − y2) dV, where H is the solid hemisphere x2 + y2 + z2 ≤ 4,…

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Q: Write the integral in rectangular coordinates, and then evaluate it. a. (xy + z²) dV where G = {(x,…

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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: 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: Set up, but do not evaluate, an iterated integral for . dv, where E is the space between two upper…

A: We have to find ∬∫EdV ,where E is the space between two upper hemispheres.

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

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

A: Given integral is,

Q: Evaluate the iterated triple integral VI+z ylzdzdy, dx =

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Q: (c) V9-x² dz dy dx 0 Jo

A: we have to find value of integration

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

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Q: Evaluate the integrals in Exercises 7. (x² + y² + z²) dz dy dx 0 J0

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Q: Use the symmetry to evaluate the double integral given below.

A: Given∫∫R(2+x2y)dA  R=[0,1]×[-1,1]

Q: Evaluate the double integral. /| 6xy2 dA, D is enclosed by x = 0 and x = V4 – y-

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Q: Find the double integral ∫∫R(2x^2−5y)dA, where R=[−1,2]×[1,3].

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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: Evaluate the triple integral ||//. z°e" dV where E is bounded by the parabolic cylinder z = 16 – y?…

A: The volume of a solid can be calculated using the triple integrals. The unit dV can be written as…

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: 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: 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 ITERATED INTEGRAL. ppy dxdy Jzy x – y 1. SS[ vzdxdydz 2.

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Q: Evaluate the triple integral. /I| ry sin(yz) dV, G where G is the rectangular box defined by the…

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Q: Evaluate the integral of (3x + 9y) dx dy, use the inner limits from 0 to y and outer limits from 0…

A: Given: The double integral ∫∫3x2+9y2dxdy, here the inner limits varies from 0 to y and outer limits…

Q: Evaluate the triple integral II ( + 3y – 32)dV, where N is bounded by 22 + y? + z? = 1, y< v3x. I o…

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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: Evaluate the triple integral a dV where E is the solid bounded by the paraboloid a = 10y² + 102² and…

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Q: Evaluate the triple integral. y dV, where E {(x, y, z) | 0 < x < 2, 0 < y < x, x – y < z < x + y}

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

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Q: Set up a double integral to find the z = x? + y? %3! %3D z = 0

A: We are asked  to set up double integral to find the volume.

Q: Calculate the double integral: S,(y + xy – 2) dA where R= [0,2] x [1,2].

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Q: Evaluate the integral: 2+u du a) b) / e"V1+ ev dy

A: Evaluate: i ∫252+u3uduii ∫ey1+eydy

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: The value of the double integral 32 dæ dy is O- 1536 O 1536 O 3072 -3072

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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 double integral. IL sy? da, D= {(x, y) I -1 s y s 1, -y – 2sxsy}

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Q: Evaluate the double integral ∬D (x2+2y)dA , where D is bounded by y=x, y=x3, and x≥0.

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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: (a) SII+y+z) dz dy dx

A: The given triple integral is: I=∫01∫01∫01 x2+y2+z2 dz dy dx

Q: Evaluate the double integral + 2y) dA, where D is bounded by y = x, y = = x°, and x > 0. 3 Answer:

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Q: Then the double integral of f(x, y) over D is f(x, y)dædy

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Q: Find the triple integral of the function f(x,y,z) = x2cos(y+z) over the cube 3 ≤x≤6, 0 ≤y≤π, 0 ≤z≤π…

A: The solution are next step

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

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

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

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

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Q: Evaluate the triple integral where E is the solid: 0≤z≤ 10, 0≤ y ≤z, 0≤x≤y. Izydv

A: Solution:

Q: Evaluate the iterates integrals 2) r*dA D = {(x, y) : 1 < a <e, 0< y S In(x)}

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