5. Evaluate the integral yze" dV; where D = {(x, y, z) : –1

Q: 2. Give iterated integrals for (xz*)dS where S is the part of the cylinder x² + y = 9 above the…

A: Given that x2+y2=9 and the part of the cylinder which is above XY plane implying that z > 0. We…

Q: Evaluate the double line integral S  of the fuinction (x − 2y + z) dS. S: z = 9 − x,  0 ≤ x ≤ 9,  0…

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Q: Evaluate the triple integral. 2xy dV, where E is bounded by the parabolic cylinders y = x² and x =…

A:

Q: 2) Evaluate the following line integral: . 0+z)dx + (x + z)dy + (x + y)dz where C consists of the…

A: C1: (0,0,0) to (1, 0, 1)x-01-0=y-00-0=z-01-0=tx=t, y=0, z=tdx=dt, dy=0, dz=dtI1=∫01[(0+t)+(t+0)]…

Q: Write down the new limits of integration for the integral -1 -1-y IIL" S(7,4, 2) dz dy dæ if the…

A: As per given tripple integral  0  ≤  z  ≤  (1 - y)  x2  ≤  y  ≤  1  -1  ≤  x  ≤  1   Thus, curves…

Q: Evaluate the triple iterated integral. 2/2 L7 xyz dx dy dz 0 Jo J-1

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

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Q: x+y+xy)dydx 2J-1

A:

Q: 13. Evaluate the triple integral: In y (z) dzdydx y2

A: Given :∫12∫1x∫y2lnyz dz dy dx=I

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

A:

Q: dy dr x+ y 33. a dz dy x² + y 34.

A: .

Q: 1. The integral of J, \z|dz along any closed path y is 0.

A: As per our guidelines, we suppose to answer only one question in case of multiple questions posted.…

Q: Evaluate the iterated integral: S", Si yz dx dz dy.

A:

Q: 1. Give iterated integrals for r (x² + yz)dV where E is in the first octant bounded by the planes: y…

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Q: Evaluate the line integral of x^3(z)ds, where C is the line segment from (0,8,2) to (7,4,6).

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Q: Evaluate the integral (x + z) dS where S is the part of the cylinder y + z2 = 4 with x E [0, 9].

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Q: Evaluate the double integral. // (x2 + 2y) dA, Dis bounded by y = x, y = x³, x > o

A: To evaluate the below double integral ∫∫Dx2+2ydA ,   D is bounded by y=x, y=x3,x≥0

Q: Evaluate the iterated integral. e² (1/xz In(z) dy dz dx

A: topic - triple integration  answer is ln(64) =6ln(2)

Q: 16. Let D-((, y, z):05zs2, 0≤ y ≤1, 05:5z+y). Find the triple integral: 72xy³ dv.

A:

Q: If  V(x,y)=(8⋅y+5)i+(9⋅x+1)j, dl=dx i+dy j and C is a path which encloses area A,  then the line…

A: We find the line integral  ∮CV⋅dl  Given that   V(x,y)=(8⋅y+5)i+(9⋅x+1)j,  dl=dx i+dy j and C is a…

Q: Evaulate the line integral of c (x^2+y^2) where c is the line segment from (-1,-1) to (2,2)

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Q: 1. Evaluate the given line integral, |(-y,x – y) · dR, where C is the upper part of x² + y? = 1 from…

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Q: Verify Green's Theorem by evaluating both integrals Lr dx + x* dy = / dA ду x² dy ax for the given…

A: In this question we verify Green's Theorem                 i.e, verify integral  ∫C y2 dx +x2 dy =…

Q: 1- Assume that x, y E R and z = x + iy E C .Calculate the following integrals using the given…

A: Note: According to our guidelines We’ll answer the 3 subparts of the question since the exact one…

Q: 2. Evaluate the given line integral, (x – y, y) · dR, where C is the line segment from (0, 1) to…

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Q: Evaluate the triple integral. y dV, where E {(x, y, z) | 0 < x < 2, 0 < y < x, x – y < z < x + y}

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Q: Evaluate the integral

A:

Q: 4. Use Green's Theorem to evaluate the line integral: f ye dx + x*y² dy, where C is the from (-2,0)…

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

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Q: #2. Evaluate the triple integral x dV, E where E is given by E = {(x, y,z) : z< x < 2z, 0 < y<x+z,…

A: Solve it

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

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Q: Evaluate the iterated integral. rIn(x) xe-Y dy dx dz 4z 434 3

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Q: 3 7z Set up the iterated double integral S S g(x,y) dy dx as dxdy such that: (iki katlı integrali

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Q: Evaluate the given line integral. | (y, –x) · dR, where C consists of the uppder part of x² + y? = 1…

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Q: In the integral STI (x² zv³) dy dz dx 1 the limits of y is from

A: We need to find the limits of y in the given integral:          ∫01∫12∫23x2zy3dy dz dx

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 double integral. 7x cos(y) dA, D is bounded by y = 0, y = x², x = 5

A: Given ∬7x cos y dydx , y=0 ,y=x2 , x =5

Q: 10.Calculate the double integral ffRXsinydydx, where R is bounded by y=0, y=x2, x=1.

A: Fubini's Theorem- If f(x, y) is continuous over the region R defined by a≤x≤b,   c≤y≤d then,…

Q: 5, find the line integrals along the given path C. In 13. | (x – y) dx, where C: x = 1, y = 21 + 1,…

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Q: Evaluate the triple integral. 5xy dV, where E is bounded by the parabolic cylinders y = x² and x =…

A: The point of intersection of the cylinder x=y2 and y=x2 is 0 and 1.

Q: 2+ y²) dz dy

A:

Q: Set up the iterated (triple) integral for the integral ]]] xy¹z³ dV where S is the tetra- S hedron…

A: We will find limits of variable and then find value of integral

Q: Set up the iterated double integral 9-9x SS dy dx of x 1. the limits . the limits of y

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Q: 4. Evaluate the double integral D where D is enclosed by the curves y = a², y = 3x.

A: First we will draw the graph for given curves from that we will find the limits of x,y as shown…

Q: Evaluate the iterated integral: 1 IIT 24a*yz² dz dy dz

A:

Q: Evaluate the iterated integral 3 In z x e' dy dz dx

A: Given,         ∫13∫xx2∫0lnzxedydzdx

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

A: