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

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

A:

Q: Find the derative of the integral from x to 2. y=(t+3)^2 dt

A: let us assume y=∫x2(t+3)2dt

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

A:

Q: Express the iterated integral in the opposite order. dy dx

A: First option is the correct option. Find the region of the integration graphically. The value for y…

Q: Compute the value of the following improper integral. If it is divergent, type D. 1 dx 0.

A: To compute the value of improper integral.

Q: Evaluate the improper iterated integral. x2 dy dx 1 + y?

A: The solution is given in the next step.

Q: Calculate the iterated integral. 3 Vs+t ds dt

A: Consider the iterated integral

Q: Evaluate the Integral (1+ z²)e²sinz dz, where C:lz=, and Compare byany two methods results. the

A:

Q: The improper integral A e B C) O D 1 if the 0 ∞ ex dx is

A: Solve the integration  From 0 to ♾️ for the integrand e-x.

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 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 integral $dz, where C: |z] = 2.

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Q: Evaluate the integral by using the substitution u = 1 + e*. 1 – e* %3D dx 1+ e*

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Q: dr Evaluate the improper integral /, Tæ – 3)3/2 or state that it diverges.

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

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

A:

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: Calculate the iterated integral 2 So Só Væ + ydædy

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Q: Evaluate the given iterated integral by reiterating it in a given order ex'dy dx dz = dz dy dx Z.

A: Integration is the process of finding the anti-derivative function of the given function.…

Q: Compute the value of the following improper integral. If it is divergent, type "Diverges" or "D".…

A:

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: 7 dx. J 2+ Vx – 4

A:

Q: Compute the integral by algebraic substitution: 7 dx. 2+ Vx – 4

A: Given: ∫72+x-4dx

Q: C * dt = 1 0.2t

A:

Q: Evaluate In x dx exactly by changing it to a dy integral.

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Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) dt…

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Q: Consider the integral 16–z² x? dz dy dx x²+y²

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Q: E valuate the improper integral Sma Xe* de Ina

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Q: Evaluate the improper iterated integral. 1/x5 y dy dx

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Q: Evaluate the integral. (Use C for the constant of integration.) pA In(t) dt * Ince) C must be in…

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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 ez+1 dz a) 0 eZ+z

A: Given Data: Integrand: ∫01ez+1ez+zdz Let u=ez+z, The derivative of u with respect to z is,…

Q: Evaluate the double integral || (x2 + 4y) dA, where D is bounded by y = x, y = x³, and x 2 0.…

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Q: Finel the integraL of finchio XSina) wher ne 5 and (0,2) by Simpsors rule 3.

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

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

A:

Q: Use a table of integrals to determine t/7t + 13 dt. JWT- 13 dt =D 7t+13

A: Here we have to evaluate I=∫t7t+13dt

Q: Evaluate the double integrals: J| (x+ y+1)dxdy

A: Given:       ∬x+y+1dxdy    =∫∫x+y+1dxdy     =∫xdx+y+1∫1dxdy       =∫x22+y+1x+Cdy…

Q: Evaluate the integral by reversing the order of integration. re* dx dy lo J3y

A:

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

A: To evaluate: ∫02∫-4-y20dx dy

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

A: Value of the given double integral is 71/84

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 integral. e sec²(8x) dx %3D +C

A:

Q: Evaluate the double integral (x2 + 6y) dA, where D is bounded by y = x, y = x³, and x > 0. Answer:

A: We have to find the value of the integral

Q: (e2x –1)2 dx 1. e 2x

A:

Q: Evaluate the improper integral if it exists dxp: 2.10 0.20 The improper integral diverges 30 2/2 40

A: Option (3) is correct. Integral diverges.

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) dt…

A: To find: The integral ∫dt1-7t6. Formula used: Power rule of integration: ∫xndx=xn+1n+1+C

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

A: Given : ∫z2+x2+y33dt