Use the Divergence Theorem to evaluate the surface integral |a? – 3y + 62) ds, S. here S is the sphere x2 + y? + z² = 9.

Q: Evaluate the surface integral F. dS where F = (4x, -5z, 5y) and S is the part of the sphere x² + y +…

A: The solution is given below:

Q: Use Green's theorem to find the surface integral of the following geometry if V = xy'i - x³yi, and…

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Q: Evaluate the surface integral F. ds where F = 5xyi +8x²j+ 5yzk and S is the surface z = ïe², 0 ≤ x ≤…

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Q: 5. Use the Divergence Theorem to calculate the surface integral SF dS, where F(x, y, z) = (xye , xy?…

A: By divergence theorem value of the surface integral is

Q: Evaluate the surface integral. ) ر م(ل 2) ds S is the part of the cylinder x² + y2 = 16 that lies…

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Q: Evaluate the surface integral fs F. dS where F = (4x, -2z, 2y) and S is the part of the sphere x² +…

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Q: Evaluate the surface integral f F. dS where F = (-2x, –5z, 5y) and S is the part of the sphere x2 +…

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Q: Verify the formula J.F., F.ndS= =JJJ₂ div div F dV G in the Divergence Theorem by evaluating the…

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Q: Use the Divergence Theorem to evaluate F. dS where F = (2²a +y?. + tan (2), a?z – 1 2, and S is the…

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Q: Evaluate the surface integral xyzdS where S is the part of the plane z = 1 + 2x + 3y that lies above…

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Q: Use the Divergence Theorem to evaluate F. ds, where F(x, y, z) = z?xi + (+ tan zj + (x²z + y2)k and…

A: We are given a closed surface integral and we have to use the Divergence Theorem to evaluate that.

Q: (a) Compute directly I = S Ss F-dS, where S is the surface of the sphere x? +y? +z? = 4 and F =…

A: X²+y²+z²=4=2² Therefore radius of sphere is 2.

Q: Evaluate the surface integral| f(x.y.z) dS using an explicit representation of the surface. f(x.y.z)…

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Q: Evaluate the surface integral. z2 S is the part of the paraboloid x = y2 + z² given by 0 sx 5 4 1 V5…

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Q: Evaluate the surface integral. ∫∫sxdS, S is the part of the plane 6x+3y+z=6 that lies in the first…

A: The plane has intercepts at (1,0,0), (0,2,0), (0,0,6). The parameterize the surface S by. where

Q: Evaluate the surface integral: S Ssx*y ds Where S is the surface of the paraboloid z = 4 – x2 – y?…

A: To evaluate the given surface integral, use the following formula. ∬SFx,ydS=∬DFx,y1+∂z∂x2+∂z∂y2dxdy

Q: -. Evaluate the surface integral z'/x2 + y?dS, where S is the surface parametrized by Ocoso, y =…

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Q: Find the area of the plane xtay-zt 10=0 that lies above the disk xy-plare

A: Given that, Area of plane is x+2y-z+10=0 It lies above the disk {(x,y)/x2+y2≤4} in x,y plane. The…

Q: Evaluate the surface integral  ffR(x+y)dS where σ is the portion of the plane z = 6 − 2x − 3y in the…

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Q: Use the Divergence Theorem to evaluate the surface integral (2x^2 + 3yz + 4xz) dS where S is the…

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Q: Evaluate the surface integral. x²z² ds S is the part of the cone z² = x2 + y2 that lies between the…

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Q: Evaluate the surface integral F. dS, where F(x, y, z) = xi+Yj+z k is taken over the paraboloid z = 1…

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Q: Use divergence theorem to evaluate F •dš where F(x,y, z) = (2x + yz)ī + 2yzj – z?k and S is the…

A: According to the divergence theorem ∬SF¯·ds¯=∫V∇·F¯dV, where V is the volume bounded by the closed…

Q: Use the Divergence Theorem to evaluate (5x + 10y + z) ds where S is the sphere x2 + y2 + z2 = 1.

A: In the given problem, S is the sphere x2+y2+z2=1Divergence Theorem:∬SF·n dS=∭Ediv F dVNow, the…

Q: Use the Divergence Theorem to evaluate (4x + 9y + z2) ds where S is the sphere x2 + y2 + z? = 1.

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Evaluate the surface integral. || x²yz dS, S is the part of the plane z = 1 + 2x + 3y that lies…

A: Given: The surface integral, ∫∫Sx2yz dS, S is the part of the plane z=1+2x+3y that lies above the…

Q: 2- Use Gauss's divergence theorem to evaluate the surface integral / ry dydz + 2y°dxdz + y?zdxdy),…

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Q: (a) Evaluate the following surface integral yex²+z² dS, where o is the portion of the surface of the…

A: Given the integral ∬σyex2+z2dS we have evaluate the given surface integral where σ is the portion of…

Q: Use the Divergence Theorem to evaluate (6x + 7y + z2) dS where S is the sphere x2 + y2 + z? = 1.

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Q: Use Divergence Theorem to evaluate [0²z?i+z?x²j+x*y²k).ds, where S is the upper part of the sphere…

A: To evaluate the below integral using the divergence theorem. ∫∫Sy2z2i+z2x2j+x2y2kds Here S is the…

Q: Evaluate the surface integral. x2z2 dS S is the part of the cone z2 = x2 + y2 that lies between the…

A: Given: The surface integral is given as, S is the part of the cone z2-x2 + y2 that lies between the…

Q: Use the Divergence Theorem to evaluate [, F• dS, where F(x, y, z) = z²x i + (y + tanz)j + (x²z +…

A: We will find out the required value.

Q: Evaluate the integral // Fn ds where F = (2r+32)i-(rz+y)3+(y² +2)& and S is the surface of the…

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Q: 2- Use Gauss's divergence theorem to evaluate the surface integral || «ry°dydz +2y°dxdz + y°zdzdy),…

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Q: Use the Divergence Theorem to calculate the surface integral f Ss F- dS where F(x, y, z)=x²yi+ry²j+…

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Q: Evaluate the surface integral , F· dS where F = (4x, –4z, 4y) and Slis the part of the sphere x2 + y…

A: Answer

Q: Use Stoke's Theorem to evaluate the line integral / 7ydx + 3zdy + dz where C is the intersection of…

A: Use Stoke's Theorem to evaluate the line integral ∫C7y dx+3z dy+ dz, where C is the intersection of…

Q: Use the Divergence Theorem to evaluate (3x + 2y + z2) ds where S is the sphere x2 + y2 + z² = 1.

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Q: (a) Compute the surface integral || a xy dS, where S is the quarter cylinder x2 + y? = 1; x, y > 0…

A: Given that The surface integral is ∬Sxy dS, where S is the quarter cylinder x2+y2=1; x,y≥0 between…

Q: Evaluate the surface integral f, F. dS where F = 3xyi + 9x²j+3yzk and S is the surface z = xe", 0≤x≤…

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Q: Use the Divergence Theorem to evaluate (4x + 7y + z²) dS where S is the sphere x2 + y2 + z² = 1.

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Q: Use the Divergence Theorem to evaluate (4x + 3y + z) dS where S is the sphere x2 + y2 + z2 = 1.

A: The divergence theorem establishes the equality between surface integral and volume integral.

Q: Use the Divergence Theorem to evaluate  F · dS,  where  F(x, y, z) = z2xi +  + ((1/3)y3 + cos z)j +…

A: Given data:

Q: Let S:x+z? = 16,0sys3 be the surface of a closed cylinder bounding a volume T.F=[z?, y, x²]. Use the…

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Q: se the Divergence Theorem to evaluate (8x + 12y + z2) ds Is here S is the sphere x2 + y2 + z² = 1.

A: To compute the below integral using divergence theorem.

Q: Evaluate the surface integral (4x² + 3y)dS where S is the part of the plane 2.x + 5y + z = 48 inside…

A: We need to calculate:∬S4x2+3ydS over the surface S,which is the part of plane 2x+5y+z=48, inside the…

Q: Jevaluate the surface integral ff, (y²z2 i+ z?x² j+ z²y²k).n ds, where S is the part of the sphere…

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Q: Evaluate the surface integral s F. dS where F (-x, -4z, 4y) and S is the part of the sphere x? + y?…

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Q: Evaluate the surface integral. || x2yz ds, s is the part of the plane z = 1+ 2x + 3y that lies above…

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