5. Using Divergence Theorem, calculate the integral /| ry dx + yz²dy + za²dz S where S is the upper hemisphere given by x2 + y² + z² = 25.

Q: 9) Use Fubini's Theorem to compute the double integral ƒƒ_ƒ(x,y)dª_where…

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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: Find the line integral of f (x, y,z) = -x + y + z over the straight-line segment from (1, 2, 3) to…

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Q: 5. . Find sSSzdv where D is the 2 solid bounded by xty'tz=4 and 2= 13x²+ 3y2. (" sce Cueam Come')

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: Evaluate the line integral, where C is the given cu curve. (x + yz) dx + 2x dy + xyz dz, C consists…

A: C consist line from A (2, 0, 1) to B(3, 3, 1) Now,

Q: 12) Find +he integral of the f(xiyia)=x+y? function on the region between the x4y1 and x?+y"= 9…

A: Convert the integral in cylindrical coordinate: ∭Vfx,y,zdxdydz=∫z=01∬1≤x2+y2≤9x2+y2dxdydz…

Q: Evaluate the line integral §. xy²dx + 2x²y dy over triangular path with vertices (0,0). (2,2) and…

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Q: dz where C:|z – 2| = 0.2 (z – 2)³(z – 5) by using (a) Cauchy's integral formula

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

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Q: Apply Green's Theorem to evaluate the integral (-5y² dx-5x² dy), where C is the triangle bounded by…

A: greens theorem

Q: 1) Evaluate the integral SRW (x,y,z)dV with W= e*-y-z where R is a rectangular box with corners at…

A: As per Bartlebys answering policy, we can answer only one question, so kindly post the remaining…

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: Use Green's Theorem to evaluate the integral 3x²y²dx + (5y³ – x³y²)dy, C

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Q: 6- Evaluate the line integral ScF · dr, where F = [xy, yz, xz] and C is the boundary of the…

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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 fz² In z dz using integration by parts 2 Onz-+ +c Oz-+ Onz-+c Oz² Inz - 2 + c

A: ∫z2lnzdz=∫(lnz)z2dz=(lnz)z33-∫1zz33dz+c=(lnz)z33-∫z23dz+c=(lnz)z33-13z33+c=(lnz)z33-z39+c=z33(lnz)-z…

Q: Evaluate the line integral §. xy²dx + 2x²y dy over triangular path with vertices (0,0), (2,2) and…

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Q: Evaluate the given line integral. I (y, –x) · dR, where C consists of 4y = x² from (-2, 1) to %3D C…

A: Line integration of the function

Q: Q2: Evaluate the Line Integral using the Proper Method/Theorem for F = [y, x', z+x] around the…

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Q: Q:4) Use Green theorem and evaluate the line integral ${Mdx + Ndy} Where M(x,y)=y², N(x,y)=x², C is…

A: See the details solution in below

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

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Q: Evaluate the double integral. [[ ×20 (2+2y) dA, D is bounded by y = x, y = 2³₁x20

A: off

Q: Use Green's Theorem to evaluate the line integral S(x² + y²)dx + (x² – y²) dy where C is the…

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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: Find the line integral of f(x,y,z) = -x+y+z over the straight-line segment from (1, 2, 3) to (0, −1,…

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Q: Evaluate the triple integral. 10x dV, where E is bounded by the paraboloid x = 5y? + 5z2 and the…

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Q: ¡(z+1)dz 3 where C is z+2|= |z+2\=% z'-4z

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Q: Evaluate the triple integral. 7x dV, where E is bounded by the paraboloid x = 5y2 + 5z2 and the…

A: Here, E is the surface boiunded by the  paraboloid x=5y2+5z2 and the plane x=5. Now, at x=5,…

Q: (1) Evaluate the triple integral I zyz dV, R where R = {(z, y, z)| 0 < z < 3, -2 <y< 1, 1< z < 3}.

A: We will use simple Integration rules to solve this triple integral.

Q: Find the line integral of f(x,y,z) = -x + y+z over the straight-line segment from (1, 2, 3) to (0,…

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)…

A:

Q: 6- Evaluate the line integral fF dr, where F = [xy, yz, xz] and C is the boundary of the hemisphere…

A: the line integral f F dr, where F = [ry, yz, xz] and C is the boundary of the hemisphere x² + y² +…

Q: (1) Evaluate the line integral of F (x, y) = (x – y, x²) over the line from (1,0) to (3, 2). |

A: evaluate line integral in following way

Q: 6. Evaluate the triple integral ry dV where E is bounded by the parabolic cylinders y = x² and r =…

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Q: 53. Verify the divergence theorem for A = 2x?y i – y² j + 4xz2 k taken over the region in the first…

A: Given : A=2x2y i- y2j + 4xz2 kbounded by y2+z2=9 and x=2

Q: Evaluate the triple integral. 8x dV, where E is bounded by the paraboloid x = 2y2 + 2z2 and the…

A: The objective is to evaluate the triple integral ∫∫∫E8xdV, where E is bounded by the paraboloid…

Q: 6. Evaluate the integral fSSp 4y dV if D is bounded by the elliptic paraboloid z = 3.x?+y²+1 and by…

A: Application of integration

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: Evaluate the double integral. 7x cos(y) dA, D is bounded by y = 0, y = x2, x = 7 %3D

A:

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: Evaluate the iterated integral. 3 (2z fIn(x) '3 xe-Y dy dx dz Jo

A: ∫13∫02z∫0ln(x)x e-y dy dx dz

Q: 2. Use the Fundamental Theorem of Line Integrals to evaluate fe F.dR, where F(x, y) = (x²y? –…

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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: O Evaluate the line integral over The Cur ve C. SCx+y+2)dx +6x +y-2)dy+ (x-y+2)dz where c is the…

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Q: Compute the integral ∮C [(cos x − 3y) dx + (2x − sin y) dy], where C is the closed curve that…

A: The region of integration C is divided into three line segments C1, C2 and C3. Let C1:y=0,…

Q: Evaluate the triple integral. 10x dv, where E is bounded by the paraboloid x = 2y² + 2z2 and the…

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Q: dl /x² + y² + 4

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

A: Consider the following graph:

Q: Evaluate the triple integral [[Scosys3 12xy²z³ dV_over the rectangular box G define by the in…

A: We have to find value of given triple Integral.