I’ve attached an image of the problem below.
I need to use the diveragance theorem to find the flux through a cylinder.
Vector field: F(x,y,z) = 4xi
By the DT, flux is equal to the triple integral of the divergence of the vector field.
The Attempt at a Solution
The divergence of the vector field is 4.
So the flux should be equal to the triple integral of 4 over the region of the cylinder.
Using cylindrical coordinates, I used the bounds 0 to 5 for z, 0 to 3 for r, and 0 to 2pi for theta.
Solving the triple integral then gave me 4(5)(3)(2pi), which was incorrect.
Can somebody help me figure out what I’m doing wrong?
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