# Flux of Vector Field Across Surface

1. Homework Statement

Compute the flux of vector field (grad x F) where F = (xz+x^2y + z, x^3yz + y, x^4z^2)
across the surface S obtained by gluing the cylinder z^2 + y^2 = 1 (x is > or eq to 0 and < or eq to 1) with the hemispherical cap z^2 + y^2 (x-1)^2 = 1 (x > or eq to 1) oriented in such a way that the unit normal at (1,0,0) is given by i.

My approach to find the flux is to take the triple integral of the gradient of F * dV. I found the gradient to be <z + 2xy, x^3z +1, 2zx^4> and I set up the integral but I am a bit confused as to what the limits should be. Should I be even taking a triple integral??

Related Calculus and Beyond Homework Help News on Phys.org
also... can I use cylindrical coordinates for the volume of the cylinder then use spherical coordinates for the volume of the cap and add them together?

HallsofIvy
How are you taking the triple integral? The "gradient of F" is a vector quantity and dV is not. I thought perhaps you were using the divergence theorem but you say nothing about the divergence of grad F (which would be $\nabla^2 F$).