Evaluate the double integral. IL sy? da, D= {(x, y) I -1 s y s 1, -y – 2sxsy}

Q: a) Integrate the following integrals i) S(4e2 + Vx) dx Sx(3+x²)10 dx ii)

A:

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

A:

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

A: ∫01∫01∫01x2+y2+z2 dz dy dx

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

A:

Q: The improper integral A e B 0 C D) 1 + ∞ [** 0 e-x dx is

A: The given improper integral is: I=∫0+∞e-xdx

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

A:

Q: 15. Evaluate the double integral (a + 6y? + bx²y) dA, where R = {(x, y) E R² : |x| + \y| < 1}.

A:

Q: || x²v d4 where D { (x,y) : xs y s 2+x, -1sxs2}. 2. sys2+x,-1<x<2}. D

A:

Q: Evaluate the double integral. dA, D = {(x, y) | 0< x < 8, 0 < ys Vx} %3D

A: The given integral is ∫∫Dyx2+1dA, D=x,y|0≤x≤8,0≤y≤x. Evaluate the given integral as follows.…

Q: 26. Evaluate the integral by reversing the order of integration. (a) (Le* dxdy (b) . ycos(x') dx dy…

A:

Q: I.Evaluate the ff. iterated integrals. • rel /2 ptan y sec y 1. x'cos' ydxdy

A:

Q: Evaluate the integral by integrating with respect to​ x, y, and z.

A: Given integral is,

Q: J xe*dx Evaluate the improper integral:

A: Given: I=∫1∞xe−xdx

Q: Use the indicated change of variables to evaluate the double integral. I/ 16(x? + y²) dA -(u + v) X…

A:

Q: Evaluate the double integral. 4y dA, D = {(x, y) | 0 s x s 1, 0 sysx} 6x + 1

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. 7x dA, D = {(x, y) | 0 <xS A, 0 s y s sin(x)}

A:

Q: 1. Evaluate the improper integral or show that it diverges. (a)/ e* dx 8. (b) / dx (c) d.r (d) /…

A: If the limit exists and is a finite number , we say that the improper integral converges .If the…

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 double integral. 7x dA, D = {(x, y) | 0 s x s a, 0 sys sin(x)}

A:

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

A:

Q: Find the double integral [[ f (x, y)dA for the function f(x, y)=1-6x²y and R:0<x<2,-1 <x< 1.

A:

Q: Evaluate the double integral. y dA, x2 + 1 D = {(x, y) | 0 s x5 8, 0 s ys V} 29727

A:

Q: Evaluate the double integral. y dA, x2 + 1 D = {(x, y) | 0 <x< 3, 0 sy s Vx} ID

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: Extend your knowledge of double integrals to evaluate the triple integral So So S**** f(x, y, z) dz…

A: Given that I=∫01∫0x∫01+x+yf(x,y,z) dzdydxTo extend the double integral to triple integral.

Q: y dA where D= { (x,y) : xs ys 2+x, -1 s x s 2 } D

A:

Q: Evaluate the double integral. y dA, x2 + 1 D = {(x, y) | 0 s x< 6, 0 s y s Vx}

A: Answer and explanation is given below

Q: Evaluate the iterated integral below. π 1 S*S'y cos (x) dy dx S. 0

A: Here we have to find given iterated integral.

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

A:

Q: Calculate the iterated integral. '1 I l'x+e-Y) dx dy Need Help? Read It

A:

Q: Set up a double integral to find the z = x? + y? %3! %3D z = 0

A: We are asked  to set up double integral to find the volume.

Q: Evaluate the improper integral Xe* dx Ina A) integral diverges ৬) C) o D) Inz In2 2

A:

Q: evaluate the iterated integral.

A: Given- ∫02∫-11x-ydydx To find- The value of the above integral.

Q: Calculate the double integral. /| x sec?(y) dA, {(x, y) I 0 s x s 8, 0 sys, R =

A:

Q: Evaluate the iterated integral below. π/4 1 S. S'y co Só 0 0 y cos (x) dy dx

A: Solution…

Q: Evaluate the double integral x° dA, where D = {(x,y) : 1 < x < e, 0 < y < In x}.

A: Evaluate the double integral as follows.

Q: Evaluate the iterated integral. ||| x*y² + z² dx dy dz 0.

A:

Q: What does the following integral calculate? f(x, y, z)dV E

A:

Q: Evaluate the double integral. dA, x2 + 1 D = {(x, y) | 0 <x< 2, 0 s y s Vx} %3D

A: Double Integral:    ∫∫yx2+1dA , D={(x,y)|0≤x≤2, 0≤y≤x}=∫02∫0x yx2+1 dy dx=∫02[y22(x2+1)]0xdx

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

A:

Q: Evaluate the double integral x* dA, where D = {(x, y) : 1 < x < e,0< y< In x}. %3D

A: The solution is given as

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

A:

Q: Evaluate the double integral J[₂x² x³ dA, where D = {(x, y) : 1 ≤ x ≤ e, 0 ≤ y ≤ ln x}.

A:

Q: x cos y dA, where D is D. x², and x = Evaluate the double integral bounded by y 0, у Answer:

A: Let's find.

Q: b) Evaluate the iterated integral In z x e' dy dz dx 3 cx2 1 x,

A:

Q: Evaluate the iterates integrals 2) r*dA D = {(x, y) : 1 < a <e, 0< y S In(x)}

A:

Q: Evaluate the iterated integral below. π 1 S. *S'y cos (x) dy 0 0 dx

A: Here in above question we have to find iterated integral.