Apply Green's Theoren to evaluate the integral. C6x+y) dx + (3xy"+4y) dy ter

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

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Q: Evaluate the iterated integral: , S (2x²y + 3ay") de dy.

A: The objective is to find the value of the iterated integral ∫-12∫242x2y+3xy2dxdy First integrate…

Q: dx Evaluate the integral V1 + 9x² 1) Which substitution will change the integral into one of the…

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Q: Evaluate the double integral f(r, 0) dA. ' π/2 re dr de

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Q: Evaluate the integral. * 64 In(y) Ap Vy J49

A: To evaluate the given integral.

Q: 2x Evaluate the improper integral J da, if it exists. (z² + 121)?

A: Use the substitution method of integration

Q: Use the Table of Integrals to evaluate the integral. (Use C for the const 6 + 12y – 36y2 dy 3 + ( 6y…

A: Given ∫y-36y2+12y+6dy⇒6∫y-6y2+2y+1 dy⇒∫y-6y2+2y+1dy , write y as 16-1122-12y and…

Q: Evaluate the integral. dA, R = [0, 6] × [0, 16] x + 1

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Q: xdx J Væ +3

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Q: Rewrite the iterated integrals in the order dydzdx 11-z- 1-z SS S f(x,y, z)dxdydz

A: Let's find.

Q: Calculate the integral f. (z-2)²2 dz, where C: |z – 1| = 3.

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Q: 3.2. Prove directly from the definition of Itô integrals that t t | B?dB, = B - | B,ds .

A: The answer is given below

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: Is dz

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Q: Evaluate the integral by making the given substitution. dp, и %3D 1 + бр2 1 + 6p2 + C

A: Solve the indefinite integral in the following way:-

Q: Evaluate the integral. dA, R X + 1 R = [0, 9] × [0, 8]

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Q: 2. Evaluate the integral using FTC Part 2. d e²-t st². t dt dx

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Q: Evaluate the integral 50 fa* (z* – 6)" de by making the substitution u = x* – 6. %3D

A: Given integral, ∫x3x4-650dx Evaluate by substituting x4-6 for u in the given integral.

Q: Use the Fundamental Theorem of Calculus to evaluate (if it exists) 4t-5 dt. If the integral does not…

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Q: Evaluate the integrals in Exercises 2. J 3 dx dx 1. 9 + x VI + 9x

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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 integral. (Use C fo ( 8x2 + 7x + 8 dx (x² + 1)2

A: Given integral is, ∫8x2+7x+8x2+12dx

Q: The improper integral A 1 B 0 C St edx is

A: To solve the improper integration.

Q: Evaluate the iterated integral f Só 6x²y° dxdy

A: Given:    ∫03∫02 6x2y3 dxdy

Q: Use this result to either evaluate the improper integral +oo 5xe dr or show that it diverges.

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Q: Use a computer algebra system to evaluate the iterated integral. V 25 - y2 y dz dx dy 25 - y2Jo

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Q: Evaluate the integrals LI Vy+I dy b. So a. 5r dr (4+r²)?

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Q: Evaluate the integral, if C is the circular path y = (1-x^2) from (1,0) to (0,1).

A: Let y=1-x2 be circular path from (1,0) to (0,1). Parameterize the above path by taking x=cosθ , then…

Q: Evaluate the double integral. Sxy² da, D is enclosed by x = 0 and x =

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Q: I dydx 1+ y? 1.

A: In the question we have to find integral.

Q: Evaluate the integral of sinº x dx from o to n/2. А. П/32 В. гп/17 С. зп/32 D. 5n/32

A: We know, 2sin2A=1−cos2A  2cos2A=1+cos2A2cosAcosB=cos(A+B)+cos(A−B)

Q: Solve the problem in a paper and upload as a pdf document. .3 Evaluate the integral SIT w?yz+v² xz +…

A: Solution: The objective is to evaluate the given integral

Q: Rewrite the iterated integrals in the order dzdyda 11-y? 1-y SS Sf(,y, z)dadzdy 0 0

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Q: Evaluate the integral

A: Solution Given ∫01x2(1-x2)52dx We need to evaluate the integral

Q: Evaluate the integral ff, (x + y) dA, where R = {(x,y): 1<x² + y² < 4, x< 0}. %3D

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Q: Evaluate the double integral Jo J-y? dxdy

A: To evaluate: ∫02∫-4-y20dx dy

Q: Evaluate the integrals ∫ e4t + 2e2t - et/e2t + 1 dt

A: Consider the following integral:…

Q: Evaluate the iterated integral I = SoS"(24y + 2) dady

A: Answer for the integral is : 14

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

A: ANSWER:

Q: Substitute u = x + 2 into u10 - zu° +c to evaluate the given integral in terms of x. 10 x(x + 2)8 dx…

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Q: Evaluate the iterated integral. T/4 '3 '3-r rz dz dr de

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Q: evaluate the iterated integral.

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Q: Find the integrals. a) R= %3D R.

A: First we have to plot region of integration.

Q: z · 3°dz

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Q: obtain a formula for any integral of the form (- a)* dz.

A: Given∫xb-1(cxb-d)kdx

Q: Use the substitution formula to evaluate the integral. the integral from 0 to 1 (8y^2-y+1)^-1/3…

A: From the given integral, Let, 8y^2-y+1 = t ----(1)Now differentiating (1), 16y -1 dy = dt32y -2 dy =…

Q: Evaluate the integral.   The integral from 1 to 4 of e^(4/x)/x^2dx

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