What is the solution to this Divergence Theorem homework problem?

[tommyp]

Homework Statement

evaluate https://instruct.math.lsa.umich.edu/webwork2_files/tmp/equations/71/7816ab9562fbe29a133b96799ed5521.png if https://instruct.math.lsa.umich.edu/webwork2_files/tmp/equations/65/11ed69ea372626e9c4cee674c8dc6f1.png 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 https://instruct.math.lsa.umich.edu/webwork2_files/tmp/equations/70/dd75ed46cf7f510c406a2b2e8cd0cd1.png

Homework Equations

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).