Suppose I use integration by substitution $x' = \phi(x)$ $$ \int_X f(x) dx = \int_{\phi^{-1}(X)} f(x') |\text{det}\phi'(x)| dx' $$ How does this formula simplify if $\phi$ is an involution $\phi(\phi^{-1}(x)) = \phi^{-1}(\phi(x)) = x$ ?
2026-03-30 02:10:14.1774836614
Integration by substitution with involution
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