Let er be the unit radial vector and r=sqrt(x2+y2+z2). Calculate the integral of F=e-rer over:
a. The upper-hemisphere of x2+y2+z2=9, outward pointing normal
b. The octant x,y,z>=0 of the unit sphere centered at the origin
The Attempt at a Solution
int(int(F dot dS))=int(int(F dot erdS))
=int(int(e-r<cos(theta),sin(theta),r> dot <rcos(theta),rsin(theta),sqrt(9-r2)>dr dtheta
The bounds of r are 0 to 3 and theta: 0 to 2pi.
I know the answer from the back of the book (18pi*(e^-3)), but I'm not getting this. Once I have the integral set up correctly, I don't have a problem evaluating it. I apologize for the annoying notation.