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## Homework Statement

Let

**e**be the unit radial vector and r=sqrt(x

_{r}^{2}+y

^{2}+z

^{2}). Calculate the integral of

**F**=e

^{-r}

**e**over:

_{r}a. The upper-hemisphere of x

^{2}+y

^{2}+z

^{2}=9, outward pointing normal

b. The octant x,y,z>=0 of the unit sphere centered at the origin

## The Attempt at a Solution

S=<rcos(theta),rsin(theta),sqrt(9-r

^{2})>

int(int(

**F**dot d

**S**))=int(int(

**F**dot

**e**dS))

_{r}=int(int(e

^{-r}<cos(theta),sin(theta),r> dot <rcos(theta),rsin(theta),sqrt(9-r

^{2})>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.