Divergence Theorem Problem

tommyp

1. The problem statement, all variables and given/known data
evaluate if and S is the surface of the region in the first octant bounded by x = 0, y = 0, below by z = 1, and above by


2. Relevant equations



3. The attempt at a solution
I used the divergence of F=5y+4z+7x.
My integral was
int(theta from 0 to pi/2)int(r from 0 to 2)int(z from 1 to 4-r^2) (5r^2sin(theta)+4rz+7r^2cos(theta)) dzdrdtheta.
I get 26pi/3+96/5, but that's not the right answer. Is my setup wrong or am I evaluating it wrong?

HallsofIvy

You set up is correct. I haven't checked the evaluation of the integral.

tommyp

Thanks for the help, but I figured it out and my setup wasn't correct. At z=1 which is the base of the region, r goes to sqrt(3) not 2. So the r integral goes from 0 to sqrt(3).