Let h(r, y) be a smooth parametrization on a region H for a surface S in...

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Let h(r, y) be a smooth parametrization on a region H for a surface S in R³. Suppose there is a continuous transform F: R H, (u, v) (x(u, v), y(u, v)) such that F is one-to-one on the interior of the region R and r:= ho F is a smooth parametrization on R for S. Show that /| Iru x reldA = || Ih, x hyldA = A(S) where A(S) is the area of S.[15 pts] Let h(r, y) be a smooth parametrization on a region H for a surface S in R³. Suppose there is a continuous transform F: R H, (u, v) (x(u, v), y(u, v)) such that F is one-to-one on the interior of the region R and r:= ho F is a smooth parametrization on R for S. Show that /| Iru x reldA = || Ih, x hyldA = A(S) where A(S) is the area of S.[15 pts]

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