Compute the double integral , xy³ dA where T is the triangle (-1,0), (0, 5), (1,0).

Q: Evaluate the iterated integral. LLL- 2 x³ y2 + z?dxdydz 0.

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Q: Compute the double integral R ye®Y dA where Ris the square -1 < x < 1, 0 < y< 2.

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

A: We are clearly given the limits of the integral. Since y limits are in terms of x so dA = dy dx

Q: x exp(-y²)dydx 0. 1

A: We have to solve given problem:

Q: Calculate the iterated integral a) [ [ (6xy² – 2x) dy dæ

A: In this question we have to find Double Integration. First find in terms of y and then in terms of…

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: Evaluate the iterated integral. 1. 7zeX dy dx dz - 0/

A: According to limit, first we integrate with respect to y then put x7 = t then solve it.

Q: Compute The double integral of a function f(x, y) = 73 over a rectangle [2, 4] × [3, 6]

A: To compute the double integral of a function fx,y=73 over a rectangle 2,4×3,6

Q: Je t ež cos (2t)dt

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Q: Calculate the double integral. JS y dA, 4xye+²y R R= [0, 1] × [0, 8]

A: Given; ∫∫R4xyex2ydA, R=0,1×0,8   As we know the common integral. ∫eax+bdx=1aeax+b+C  And ∬dA=∬dxdy…

Q: Calculate the iterated integral a) (6xy² – 2r) dy dr

A: I am going to provide solution of 2nd question. Kindly repost the other one.

Q: Evaluate the iterated integral: S", Si yz dx dz dy.

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Q: Find the line integral of F(x, y, z) = x³i + yj+ zk along th the origin to the point (3, 2, 6). F.…

A: See the details solution in below

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

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Q: Find the integral of r(t) = (3t2 + 4t, 2, e') from 0 to 1.

A: Consider the following vector: rt=3t2+4ti^+2j^+etk^ Integrate the above vector:…

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: Express the integral Js(x) dx in terms of Jo, J1 and J2.

A: Bessels function identity:  Jn+1(x)=2nxJn(x)-Jn-1(x) Given: ∫J5(x)dx

Q: Calculate the double integral. 9x sin(k + y) dA, R = 0, 풍핑x [o, 플]

A: First we will evaluate the inner integral wrt 'y' and then evaluate wrt 'x'.

Q: Evaluate the integral f, (5x + 6y²) dA, where R = {(x,y)|0 < x < 4,0 < y < 3}.

A: Given integral is ∬R (5x + 6y2) dA Where R =  (x, y) | 0≤x≤4, 0≤y≤3

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 | t(sec t2)4 dt

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Q: 10 Why is J 5 Vx-5 11 =dx an improper integral?

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Q: Estimate the value of the integral 4- x²y2 dA, S = {(x,y)| x² + y? 0} |

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Q: Calculate the integral f. dz, where C: |z| = 1. (2z+1)(2-2)

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Q: 1 (x²+y*) dx dly -1 2

A: Consider ∫-11∫24(x2+y2) dx dy = ∫-11x33+xy224 dy = ∫-11643+4y2-83-2y2dy = ∫-11563+2y2dy =…

Q: Find the complete integral of 1 az z dx, 1 dz z dxz 1 dz =x1 x2 X3. z dxz

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Q: Evaluate the integral.

A: Given, ∫49lnyydyLet, I=∫49lnyydy Integrate by parts we get,…

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

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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 line integralſ (x + 2y) dx + x² dy, where C consists of line segments from (0,0) to (2,…

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Q: Find the integral of f(r, 0) = where 1 <r <3, 4r2,

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Q: Calculate the double integral. 8x dA, R = [0, 8] × [0, 1] 1 + xy

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Q: Evaluate the iterated integral. rIn(x) xe-Y dy dx dz 4z 434 3

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Q: Evaluate the iterates integral: S, (x- y) dy dx

A: By integration property

Q: Use symmetry to evaluate the double integral. x' dA, R = [-4, 4] × [0, 5]

A: Replace dA by dxdy x is from -4 to 4 y is from 0 to 5

Q: Calculate the double integral. Te 1+ xy бх dA, R = [0, 6] × [0, 1] 1 + xy

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Q: Evaluate the integral x2 ds where C is the portion of x2+y2=4 from (0,2) to (-2,0).

A: ANSWER:

Q: Calculate the iterated integral. '64 Y)dy dx

A: Given that a double integration and we solve this using general rule of integration. Here i attached…

Q: Evaluate the integrals 1 (x² + y² + z²) dz dy dx 0, 0,

A: The value of the integral is, 1. The detailed solution is as follows below:

Q: Evaluate the line integral along the curve C. S-s - ydx + xdy, C: y² = 3x from (3,3) to (0,0) O 4 O…

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Q: 2+ y²) dz dy

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Q: Evaluate the integral: (In z)6 dz %3D

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Q: Calculate the double integral. ∫∫ ey ^2 dA, D= {(x,y)| 0≤ y ≤3, 0≤ x ≤ y}

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Q: Find the double integral ff (x² + y² do, over R={(x, y):-1≤ x ≤ 1,0 ≤ y ≤ 2}. 1.

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

Q: Evaluate the double integral. dA, D = {(x, y) |0Sx< 5,0 < ys Vx} x2 + 1

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Q: Evaluate the line integral along the curve C. S-Tabe − ydx + xdy, C: y² = 3x from (3,3) to (0,0) O O…

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Q: Evaluate the triple integral,   4x dV, where E is bounded by the paraboloid x = 5y2 + 5z2 and…

A: To calculate the value of the triple integral under the given terms

Q: Find the integral of f (z2 +x2 + y33) dt.

A: Given : ∫z2+x2+y33dt

Q: dx, Evaluate the improper integral : [° 6x³e-3x°

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