(adsbygoogle = window.adsbygoogle || []).push({}); 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 [tex]\sigma[/tex] has two parametrizations,r(s,t) for (s,t) in the regionRof st-space, and alsor(u,v) for (u,v) in the regionTof 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 [tex]\frac{\partial(u,v)}{\partial(s,t)}[/tex] is positive at every point (s,t) inRUse the change of variables formula for double integrals to show that computing the flux integral [tex]\Phi=\int\int Fnds [/tex] 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?

Thanks for your help.

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# Homework Help: Flux through two parametrized surfaces

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