- #1
Treadstone 71
- 275
- 0
Verify the divergence theorem by evaluating both the surface and the volume integrals for the region bounded by x^2+y^2=a^2 and z=h for the vector field:
\mathbf{F}=(x,y,z)
For the volume integral, it's easy. Since divF =3, it's just 3\pi a^2h. However, for the surface integral, I divided it into 3 parts. The top and bottom discs, and the side of the cylinder. It's the side that I'm having trouble with:
F*N=\sqrt{x^2+y^2}, but how should the parameters vary?
\mathbf{F}=(x,y,z)
For the volume integral, it's easy. Since divF =3, it's just 3\pi a^2h. However, for the surface integral, I divided it into 3 parts. The top and bottom discs, and the side of the cylinder. It's the side that I'm having trouble with:
F*N=\sqrt{x^2+y^2}, but how should the parameters vary?
