Surface integrals in spherical coordinates

[jbusc]

Hi,

I am studying for finals and I'm having trouble calculating flux over sections of spheres. I can do it using the divergence theorem, but I need to know how to do it without divergence thm also.

The problem is, when calculating a vector field such as F(x, y, z) = <z, y, x>, say over the unit sphere (x^2 + y^2 + z^2 = 1), I always end up with weird terms like sin^3(phi) and cos^2(phi)sin(theta) that must be integrated

So, is this normal? Should I memorize integrals for sin^3(phi) and such, or is there an easier method?

thanks

 

[0rthodontist]

Integrating sin^3(phi) is not difficult. You know sin^3(phi) = sin^2(phi)*sin(phi) = (1-cos^2(phi))sin(phi). Then just use u-substitution with u = 1-cos^2(phi)

 

[jbusc]

*sigh* I guess it is easy. For some reason it just seems...unnecessary...