2. Evaluate the following Integral by using suitable method: 2y3 + y y4 + y2 + 1 dy -

Q: Q4 Evaluate the double integrals: [(x + + y+1)dxdy

A: Value of the giveen integral is

Q: b) Calculate the following integrals x²(3x³ + 2)²dx (i) (ii) sin3x e³x dx (ii) (2x22+₁ +*²+2) dx S…

A:

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

A:

Q: x exp(-y²)dydx 0. 1

A: We have to solve given problem:

Q: Evaluate the double integrals ffe Se-x²-² dxdy, where D = {(x, y) | x² + y² ≤ 4, x ≥ 0, y ≥ 0}.

A:

Q: Evaluate the iterated integral. 17 [₁₁/₁² (x² + y²) dx dy = i 17 LL" (2² + y²) dx dy

A:

Q: Evaluate the iterated integrals. 2 yz b. So So So xyz dx dy dz Jo 0 0

A:

Q: Which of the following integrals will yield In u+ C? A. SE B. S- x+1 D. S dx xdx C. S 2rdx = x+1 O…

A: From the following integrals will yield ln u+C Note:     Multiple questions are given, we are answer…

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: B- Evaluate the following double integrals: .2 .4 1) | (x+ 3y x²)dy dx

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

Q: Evaluate the double integral: To L 0 y x7 +1 y¹/3 x7 dx dy.

A: The given integral is: I=∫08∫y132yx7+1dxdy   So, The limit of the x varies from y13 to 2. The limit…

Q: evaluate the iterated integral.

A: ∫03∫-20x2y-2xy dy dx=∫03∫-20yx2-2x dy dx=∫03x2-2x dx∫-20y dy

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

A:

Q: Evaluate the iterated integral. (x² – y²) dy dx -1J-4

A:

Q: Evaluate the integrals

A: We need to find the integral.

Q: Evaluate the integrals

A: Given: ∫-3-1y5-2yy3dy for evaluating this limit we first separate terms then integrate it

Q: 24. Evaluate the integral: ," dy y2+2y-3

A:

Q: Evaluate the double integral : (y – 8x) dæ| dy

A:

Q: 4. Use the substitution formula and evaluate the following integral: dy -1 y/4y² – 1

A: This question is based on the substitution, make a substitution for y such that the denominator part…

Q: Evaluate only two of the following integrals: -16 In y a) S 8x² sin(4x) dx dy 4/y b) Jg 4Vý

A:

Q: 15. Evaluate the following integrals: (b) , Tax+1)3/2 (c) f, (8)05xdx. 30 8 dx (a) J 7x+5)1/3 ' -dx,

A:

Q: Evaluate the integral [x²y³² (x²y + xy² + y²²)dxdy dz 001

A: The given triple integral is ∫01∫02∫13x2y3x2y +xyz+yz2 dx dy dz. First integrate with respect to x…

Q: Evaluate the iterated double integral: x+4 sin (y – 3y?) dy d.x x+4

A:

Q: Evaluate the iterated integral Vy exp dx dy 0.

A: ∫14∫0y exydx dy = ∫14yexy0y dy                                       = ∫14ye - 1 dy…

Q: 1-Evaluate the following integrals 1/4 a) d x 4. b) SyV4-y dy

A: Consider the given information: To evaluate the integrals.

Q: Evaluate the following integrals: a) b) ex² Jy/2 dx dy dy dz dx 2y

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

Q: Evaluate the double integral. |/ (2x + y) dA, D = {(x, y) | 1 sy< 2, y – 1 < x < 1}

A: Evaluate the double integral  ∫∫D2x+y dA     , D=x,y|1≤y≤2,y-1≤x≤1

Q: Evaluate the integrals. ∫y2(3y3 + 1)4 dy

A: Since, we have to evaluate the integral given below:-∫y2(3y3+1)4 dy -(i)

Q: Q4 Evaluate the double integrals: ||x+y+1)dxdy

A:

Q: 2e^xdx-3e^ydy=0   What is y'? What is its integral?

A:

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

A:

Q: Evaluate the improper integral A 0 (B 4 C diverges 2 D 9 mit 2 3 -2 X 3 dx

A:

Q: 1. Compute the given integral. Using Substitution Method 5x-12 dx = +C 5x2-24x-1 *

A:

Q: Evaluate the integral. V3 9earctan(y) dy 1 + y2

A:

Q: Evaluate the iterated integral. SS 5x= dy dz dz = 0 0 0

A: Integration is evaluated by integrating first y then x then z.

Q: Evaluate the integral 1. ( (y - 1)(2y + 1) dy

A:

Q: Evaluate the iterated double integral: x+4 sin (y³ – 3y?) dy d.x - x+4

A: Let's find.

Q: Q15. Evaluate the integrals 1. (x² + y² + z?) dz dy dx

A: We have to evaluate the integral.

Q: evaluate the iterated integral.

A:

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

A:

Q: 1. Evaluate the integral Vi-x² ex?+y*dydx.

A: 1. The given integral is, ∫01∫01-x2ex2+y2dydx. Convert the integral into polar coordinates as…

Q: 1. Use Numerical methods to approximate the following integrals (a) (x +y)dxdy , n = m = 3

A: Trapezoidal rule: ∫cd∫abf(x, y)dxdy=h2fa, y+2fa+h, y+fa+2h, y+⋯+fa+n-1h, y+fb, ydy, where h=b-an.…

Q: Calculate the following integral

A: Given,

Q: 2 Evaluate the iterated integrals. 2 (x + 3) dy dx 0, 6. y sin x dy dx

A:

Q: 3. Find following integrals using method of substitution: Sze z dz a. 2 x2 b. S /1+x

A: Consider the provided integral, ∫ze-z22dz Find the expression for this integral using substitution.…

Q: Evaluate the integral. X √ ² ₁x + (x + 16y) dy

A:

Q: Evaluate the iterated integral. 5x (x + y²) dy dx J4x

A:

Q: Evaluate the iterated integral. (x² – y²) dy dx J-4

A: Given the double integrationI=∫−11∫−44(x2−y2)dydx

Q: Evaluate the iterated integral. 16 - y2 4 (x + y) dx dy

A: