# Homework Help: Flux through two parametrized surfaces

1. May 17, 2010

### frozenguy

1. The problem statement, all variables and given/known data
Show that the flux through a parametrized surface does not depend on the choice of parametrization. Suppose that the surface $$\sigma$$ has two parametrizations, r(s,t) for (s,t) in the region R of st-space, and also r(u,v) for (u,v) in the region T of uv-space, and suppose that the two parametrizations are related by a change of variables: u = u(s,t), v = v(s,t). Suppose that the Jacobian determinant $$\frac{\partial(u,v)}{\partial(s,t)}$$ is positive at every point (s,t) in R Use the change of variables formula for double integrals to show that computing the flux integral $$\Phi=\int\int Fnds$$ parametrization gives the same result.

3. The attempt at a solution
So if the Jacobian determinant is positive at every point in R, what does that mean for T? That it is positive as well?
Have I used to the change of variables formula to show that computing the flux using either parametrization gives the same result?