Question
Asked Nov 27, 2019
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Find the flux of the vector field V(x, y, z) 3xyi 8x2yj zk out of the unit sphere.
MarsVectorCalc6 7.6.014
+-/1 points
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My Notes
Evaluate the surface integral
F n dA, where F(x, y, z) i +j + z(x2 + y)2k and S is the surface of the cylinder x+ y s 1, 0 S z
4. (Give this surface an outer normal.
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Find the flux of the vector field V(x, y, z) 3xyi 8x2yj zk out of the unit sphere. MarsVectorCalc6 7.6.014 +-/1 points Ask Your T My Notes Evaluate the surface integral F n dA, where F(x, y, z) i +j + z(x2 + y)2k and S is the surface of the cylinder x+ y s 1, 0 S z 4. (Give this surface an outer normal.

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Expert Answer

Step 1

The flux through the surface S and solid region E of a vector field F is calculated by,

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SF as=dvFav div FdV

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Step 2

Here V(x,y,z) is given by,

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(3xy ,8y.)

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Step 3

Find div F for the divergence theorem and substitute, x2+...

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o(3xy2) (8ry) o(-) div F =- =3y +8r2 +3 3(x +y? +z)+ 5x* = 3r2 5

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