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

Q: The improper integral A) 0 B 1 C D e +∞o Sto 0 8 ex dx is

A: On solving this we will get

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: Evaluate the integral, AP where, E lies between spheres +y + z = 2 and a + y + = 3. for a 20

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Q: 0. Everlueik he integral (ez)Esmz dz, where Ci12|=1, by any and two methods Compare the geselts.

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

A: Use the substitution method of integration

Q: Evaluate the integrals in Exercises  by making a substitution(possibly trigonometric) and then…

A: since you have posted multiple questions so I'll solve first one for you , for rest question's…

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 integrals: B:S, S' S'(x² + y² + z²)dz dy dx

A: ∫01∫01∫01x2+y2+z2 dz dy dx

Q: Express the integral in terms of the variable u, but do not evaluate it. In c dr; u = In x rels In c…

A: To determine: where  u = lnx

Q: where d! x*ry*< a² 2.

A: Change in polor coordinate.

Q: Evaluate the Integral dz 1. S z²+4z ANSWER: 1. - In + C 4 |z+4

A:

Q: Next, use the substitution w = x² – 9 to find the integral: SZ, da = S 1/w dw = In(w) +C =…

A:

Q: Evaluate the integral *(* – 10)"dz 6 by making the substitution u = 1 z° – 10- +C

A: ∫un du = un+1n+1+C ; where 'C' is an integration constant.

Q: Evaluate the iterated integral. yz dx dz dy 45 в) 34 47/3 D) 5

A:

Q: Consider the triple integral I = S S“(y² – 6z)dydzdx. -

A: ∫02∫x21∫0xzy2-6zdydzdx=∫02∫x21z3x33-6z2xdzdx=∫02x31-x812-6x13-x63dx=31.88888…

Q: Evaluate the integral. * m/6 cos(z) dz sins (z) Jn/2

A: Given,          ∫π2π6coszsin5zdz

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: Is dz

A:

Q: Apply Cauchy integral formula to find the value of the integral ſ. AG-DE dz; where C: |z| = 3. 2z-1

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Q: Evaluate the integral J 2x(x² + 6)¨ dx using the substitution u = x2 + 6. | 20 (a? + 6) " d.x +C

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Q: Evaluate the integral using the given substitution. 18(6x- 2)6 dx , u = 6x - 2 0.(6x - 2) +C O (6x -…

A: The given integral is ∫186x-2-6dx and  u=6x-2

Q: The integral dz is equal to 2e + C. Select one O True OFalse

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Q: Calculate the iterated integral 2 So Só Væ + ydædy

A:

Q: 4 ∞ dy dx J I+ 4? 2. 00

A: To find the integration

Q: Evaluate the integral. r 81 In(y) dy Vy 64

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

A: To solve the improper integration.

Q: Evaluate the integrals:

A: Integration: ∫sect dt=ln|sec t +tan t|+c∫u.v dx=u.∫v dx -∫[ddx(u).∫v dx]dx   [ by parts]

Q: Evaluate the integral. r81 In(y) dy Vy 64

A:

Q: Use the fact that cos(z) = R(eiz) = (eiz + e-iz)/2 to find the integral of (e3xcos(4x))dx.

A: Here the given integral in not in the complex form so we calculate the integral as it is given in…

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

A:

Q: Make the indicated u-substitution, and then use the Table of Integrals to evaluate the integral. e6x…

A:

Q: Evaluate the integral f 2x (x² + 2)° dx using the substitution u = x? + 2. | 20(a* + 2)" de +C

A: The given integral is: I=∫2xx2+26 dx

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

A:

Q: Rewrite the iterated integrals in the order dzdydx 11-y? 1-y SS S f(x, y, z)dædzdy 00

A: The given integral is: ∫01∫01-y2∫01-y f(x, y, z) dx dz dy

Q: , evaluate the given double integral. I sinxcos(y – n)dxdy 10.

A:

Q: Calculate the integral Sa-ydA D where D = {(r, y)|0 < < 2y < 2}. %3D

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Q: Evaluate the integral Sr 8ry dA, where Ris the triangle 8x + y 0, y > 0.

A:

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

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

A:

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

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Q: Compute the integral VI-y² In(a? + y? + 1)dædy 1-y² y=-1 Jr= and enter the solution below with up to…

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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: 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: The improper integral J 1 r2-4x-5 dx is given by:

A: In this question, we reduced the integral into trigonometric form by using suitable transformation.

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

A: First we have to plot region of integration.

Q: The Value of the integral s s xy Jx*+ye dydx is 15 ITrue False 日回

A:

Q: Evaluate the triple iterated integral x dz| dy d

A: Solution of given question is followed by:

Q: Evaluate the integrals .SiPi+7 j+(t+1)k] 4 S (sinti+(1+cost)j] -a4

A: In the given question, we have to find the integral of  ∫01[t3i+7j+(t+1)k] ∫-π4π4[sinti+(1+cost)j]

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