mathstresser
Junior Member
- Joined
- Jan 28, 2006
- Messages
- 134
Use the divergence theorem to calculate the surface integral \(\displaystyle \L\\\int_{S} F dot ds;\)that is, calculate the flus of F across S.
\(\displaystyle \L\\F(x,y,z)= x^4i- x^3z^2j+ 4xy^2zk\)
\(\displaystyle S: x^2 + y^2 = 1, z=0, z=x+2\)
\(\displaystyle div F= 4x^3 + 0 + 4xy^2 = 4x^3 + 4xy^2\)
Now I do the triple integral of the divergence of F, but I don't know what to do after that.
In the only other problem I've done, the divergence was 1 and I took that times the volume of the object (which happened to be a sphere)... So I don't knoww what to do in this case.
\(\displaystyle \L\\F(x,y,z)= x^4i- x^3z^2j+ 4xy^2zk\)
\(\displaystyle S: x^2 + y^2 = 1, z=0, z=x+2\)
\(\displaystyle div F= 4x^3 + 0 + 4xy^2 = 4x^3 + 4xy^2\)
Now I do the triple integral of the divergence of F, but I don't know what to do after that.
In the only other problem I've done, the divergence was 1 and I took that times the volume of the object (which happened to be a sphere)... So I don't knoww what to do in this case.