Calculate the double integral 3 dædy D x4 D= {(x, y)| 1< < 3, 3 –x < y < 6 –x} D

Q: Evaluate the iterated integral. 8 4 b²b²x + (x + y) dy dx

A: Given query is to find the value of the integral.

Q: Evaluate the double integral. (2х + у) dA, D = {(x, y) | 1<ys 4, y – 3 <x< 3}

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Q: Evaluate the double integral / (a (x² ,2 + 8y) dA, where D is bounded by y = x, y = x°, and x > 0.

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Q: 15. Evaluate the double integral (a + 6y? + bx²y) dA, where R = {(x, y) E R² : |x| + \y| < 1}.

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Q: Use symmetry to evaluate the double integral. 4xy 1+ x2 dA, R= {(x, Y) | -4 s x s 4,0 s y s 1}

A: When the upper and lower limits of definite integrals become same, the result is zero irrespective…

Q: Calculate the improper integral 2 x+y+ z" . e 2 2 2 -x-y -z 2 8. dxdydz.

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Q: where d! x*ry*< a² 2.

A: Change in polor coordinate.

Q: evaluate the iterated integral.

A: Evaluate: ∫-10∫-11 x+y+1 dx dy

Q: 2x Evaluate the improper integral J dx, if it exists. (x2 + 64)2

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Q: Evaluate the double integral 2.x² – xy)dA, D = {1<r< 2, <o<n} - D

A: we have to find the integral

Q: Evaluate the integral: ∭D(x2+y2+z2) dxdydz, where D is defined by x2+y2+z2≤2.

A: Given:-                               Evaluate the integral: ∭Dx2+y2+z2dxdydz…

Q: Calculate the double integral 2 dædy D= {(x, y)| 3< ¤ < 5, 5 –¤ < y < 8 –x} D x3 Enter the exact…

A: We need to evaluate double integral.

Q: 1. Find a particular integral for d²y dy dr +4- + 3y = r? dr2

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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: Evaluate the double integral ∫∫R  y / (1 +xy)2 dA, where R= [0,1]×[0,1].

A: Given integral is  where  R= [0,1]×[0,1].

Q: Calculate the double integral where R = [1,2] × [-1,1]: R xeᎩ dᎪ

A: Sol:- It can be re-written as :- ∫12∫-11xeydydx......................(1)First siolve this…

Q: Evaluate the double integral x° dA, where D = {(x, y) : 1 < æ < e,0 < y < In x}.

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Q: Consider the integral 3 4х f (x, y) dy dx 0, Evaluate the integral for f (x, y) = 5x²y

A: Given Data: Integrand: ∫03∫04xfx, ydydx Function: fx, y=5x2y3 Integrate the function. ∫03∫04xfx,…

Q: Find the double integral [[ f (x, y)dA for the function f(x, y)=1-6x²y and R:0<x<2,-1 <x< 1.

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Q: Evaluate the iterated integral. 4 (x² – 2y²) dx dy %3D

A: We need to evaluate the following integral ∫12∫04x2-2y2dx dy

Q: Evaluate the double integral. dA, D = {(x, y) | 0 < x < 9, 0sys Vx} ID x² + 1

A: The double integral is given by:

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 double integral x cos y dA, where D is bounded by Y = 0, y = x², and x - 2. Answer:

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Q: Solve the double integral J, J, (1+ xy)² dydx In n(금) O 2ln(5) – In(3) O In(3) – 4ln(5)

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Q: 3 The integral ³³ g(x, y) dxdy is equivalent 3 to ₁ ³x g(x, y) dydx

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Q: Evaluate the double integral. бу dA, 2x5 + 1 D = {(x, y) | 0 <x< 1, 0 < y s x²}

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Q: 1š + z² + 2 f(z) = Calcule S f(x) dz.

A: Given data: The expression for the given function is f(x)=(x5+x2+2)/(x3-x). The integral of the…

Q: Q2/(a): Evaluate the double integral , 3xy dA over the rectangle dA = dydx} R {(x, y): -3 x< 2,…

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Q: Evaluate the triple integral and confirm that 2 2 dx dy dz = = In 35, where D is the rectangular box…

A: We will prove the given statement .

Q: Evaluate the iterated integral. 2 *4z [In(x) f Jo xe Y dy dx dz

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Q: 3. Show that, in the region D: 1< x<e, 0<y<In(x), the following double integral 3e4 + 1 x3 dA 16

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Q: 3 7z Set up the iterated double integral S S g(x,y) dy dx as dxdy such that: (iki katlı integrali

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Q: Evaluate the iterated integral. 6. 8. (x + y + z) dx dz dy

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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 double integral. 8xy2 dA,    D is enclosed by x = 0 and x = (4-y^2)^1/2

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Q: Evaluate the iterated integral. 16-y² ST Jo (x + y) dx dy

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Q: evaluate the iterated integral.

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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 double integral for R: 0<y<1,0<x<y² . Sly e*dxdy .

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Q: Evaluate the double integral x* dA, where D = {(x, y) : 1 < x < e,0< y< In x}. %3D

A: The solution is given as

Q: Set up the iterated (triple) integral for the integral ]]] xy¹z³ dV where S is the tetra- S hedron…

A: We will find limits of variable and then find value of integral

Q: 4. Evaluate the double integral D where D is enclosed by the curves y = a², y = 3x.

A: First we will draw the graph for given curves from that we will find the limits of x,y as shown…

Q: Evaluate the double integral J[₂x² x³ dA, where D = {(x, y) : 1 ≤ x ≤ e, 0 ≤ y ≤ ln x}.

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Q: b) Evaluate the iterated integral In z x e' dy dz dx 3 cx2 1 x,

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Q: The improper integral A) e (В (C) O (D) 1 8 Stoe ex dx is

A: We have to find the value of the integral

Q: Evaluate the iterated integral 3 In z x e' dy dz dx

A: Given,         ∫13∫xx2∫0lnzxedydzdx

Q: Evaluate the iterated integral. V 4 - y2 (x + y) dx dy

A: