Calculate the integral f. dz, where C: |z| = 1. (2z+1)(2-2)

Q: Compute the double integral of f(x, y) = 12x³y over the given shaded domain D. /| 12x³y dA = 2 1 2 3…

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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 integrals in Exercises using integration by parts.

A: The integral given to us is  ∫y16-y2dy

Q: 'ind the line integral of F(x, y) = (x² – y² , 2xy) = (P, Q) along the boundary of the rectangle %3D…

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

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Q: Evaluate the double integral 2.x² – xy)dA, D = {1<r< 2, <o<n} - D

A: we have to find the integral

Q: Evaluate the integrals in Exercises 1. esin (e) dx 2. e cos (3e – 2) dt

A: Given the integration I=∫exsin(ex)dx

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

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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: Evaluate |- e*dz where c is |z|=3 using Cauchy's integral formula „(1+2),

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Q: Evaluate the integrals in Exercises 7. (x² + y² + z²) dz dy dx 0 J0

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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.

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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: Find the double integral ∫∫R(2x^2−5y)dA, where R=[−1,2]×[1,3].

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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: Compute the double integral of f(x, y) = 10x*y over the given shaded domain D. || 10x*y dA = ( I 2 3…

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Q: Evaluate the double integral x cos y dA, where D is bounded by y = 0, y = x², and x = 5.

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

A: To solve the improper integration.

Q: Use symmetry to evaluate the given integral. (7 Зх + 2y) dA, - where D is the region bounded by the…

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Q: The double integral T f(x)g(y)dydx,where a,b.c, and d are constants, is equal to

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Q: Evaluate the integral, z' dv where, E lies between spheres2+y += 2 and +y += 3, for z 2 0

A: According to question,E lies between spheres,x2 + y2 + z2 = 2,andx2 + y2 + z2 = 3,x≥0

Q: Evaluate the integral p.v. J. r+1 e2ix -dx.

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Q: Estimate the double integral_R  (3xy^(2)+2x^(2)) dA where R= [0,1] x [0,1] by diving R into four…

A: We need to evaluate integral.

Q: Compute the integral fo S x cos(xy)dxdy

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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 || (x2 + 4y) dA, where D is bounded by y = x, y = x³, and x 2 0.…

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Q: Find the integral by residue theorem I = S, z+7 dz 0 z6+1 %3D

A: Given integral is I=∫0∞z+7z6+1dz Consider the contour C real axis from -R to R Let ∫Cfzdz, where…

Q: Calculate the integral / F. dr where F(x, y) = (xy? + 3x2y) i+ (x + y)x²j is conservative, and C is…

A: Answer

Q: Evaluate the integral

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Q: Evaluate the triple integral and confirm that 2 2 dx dy dz = = In 35, where D is the rectangular box…

A: We will prove the given statement .

Q: Calculate the double integral: S,(y + xy – 2) dA where R= [0,2] x [1,2].

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Q: e2z Sc Where C is Z = |3 Q5- The value of the integral J. =......... (Z+1)4

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

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Q: Evaluate the integral: 2+u du a) b) / e"V1+ ev dy

A: Evaluate: i ∫252+u3uduii ∫ey1+eydy

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 (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: Evaluate the double integral [[ cos(x + y) dA, where R is the region bounded by the lines y = r and…

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Q: Evaluate the line integralſ (x+2y) dx + x² dy, where C consists of line segment from (0, 0) to (2,…

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

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

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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: 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: Evaluate the integral   ∫∫R sin(x2 + y2)dA,   where R={(x, y)|-1√(1-y2 )≤ x ≤ 0, -1 ≤ y ≤ 1}

A: Evaluate the integral∫∫Rsinx2+y2dAwhere R=x,y/-1-y2≤x≤0 and -1≤y≤1

Q: Compute the line integral of f = x? - y, along C:x² + y? = 4 in the first quadrant from (0,0) to…

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

Q: The double integral f(x)g(y)dydx ,where a,b.c, and C d are constants, is equal to

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

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