football273
New member
- Joined
- Dec 6, 2008
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- 1
Question: Use the divergence theorem to evaluate the flux of F across S if F=<3xy,5yz,4xz> and S is the surface of the region in the first octant bounded by x = 0, y = 0, below by z = 22, and above by z=25-x^2-y^2
Here is what I have so far...
div(F) = 3y+5z+4x and this becomes
triple int(3y+5z+4x)dV
The surface is a paraboloid that opens downwards from z=25. I converted it to cylindrical coordinates so the integrand becomes
(3sin(theta)*r+5*(25-r^2)+4*cos(theta)*r)r dz dr d(theta) and I integrated for 22<=z<=(25-r^2), 0<=r<=sqrt(3), 0<=(theta)<=(pi/2)
This problem is very frustrating because I know I am making a very boneheaded mistake. I have no clue where I'm messing up.
Any help is much appreciated.
EDIT: Nevermind, I figured it out
Here is what I have so far...
div(F) = 3y+5z+4x and this becomes
triple int(3y+5z+4x)dV
The surface is a paraboloid that opens downwards from z=25. I converted it to cylindrical coordinates so the integrand becomes
(3sin(theta)*r+5*(25-r^2)+4*cos(theta)*r)r dz dr d(theta) and I integrated for 22<=z<=(25-r^2), 0<=r<=sqrt(3), 0<=(theta)<=(pi/2)
This problem is very frustrating because I know I am making a very boneheaded mistake. I have no clue where I'm messing up.
Any help is much appreciated.
EDIT: Nevermind, I figured it out