Theorem (Change of variables formula) Let $A \subset \mathbb{R}^{n}$ be an open set and $g:A\to \mathbb{R}^{n}$ be an [[Function from R to R is strictly monotonic iff it is injective|injective]] and continuously differentiable. If $f:g(A)\to \mathbb{R}$ is integrable then $\int_{g(A)} f = \int_{A} f \circ g \; \lvert \det \partial g \rvert $