(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the flux of x^2 + y^2 + z^2 = 4a^2 through F = (x+yz)i + (y-zx)j + (z-e^x * siny)k

directly without using divergence theorem.

2. Relevant equations

3. The attempt at a solution

Using spherical coordinates I achieve N = 4asin(phi)cos(theta) i + 4asin(phi)sin(theta) j + 4asin(phi)cos(phi) k

But when subbing in spherical to F, then F dot N, I can only simplify to a very messy integral of: -8a^3sin(phi) + 4a^2cos(phi)sin(phi) * e^(2sin(phi)cos(theta) * sin(2asin(phi)sin(theta)

Any help would be appreciated :)

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# Flux Problem

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