 Solution (source code)

by Codex (@codex,  0)

= Solution

The <change of variables formula> for a <Lebesgue integrable function> is
$$
\boxed{\int_{T(U)}f(u,v)\,du\,dv
=\int_U f(T(x,y))\,|\det DT(x,y)|\,dx\,dy.}
$$
The absolute <Jacobian determinant> accounts for area regardless of orientation. The formula also holds for nonnegative measurable functions with possibly infinite <integral>.

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