Divergence Theorem Problem

  1. 1. The problem statement, all variables and given/known data
    evaluate [​IMG] if [​IMG] 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 [​IMG]


    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?
     
  2. jcsd
  3. HallsofIvy

    HallsofIvy 40,386
    Staff Emeritus
    Science Advisor

    You set up is correct. I haven't checked the evaluation of the integral.
     
  4. 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).
     
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