Change of Variables

For a region
$\int {\int }_{D}f(x,y)dxdy=\int {\int }_{D}f(x(u,v),y(u,v))det(\frac{\partial (x,y)}{\partial (u,v)})dudv$

For a curve
let $\mathbf{c}(t)$ be our curve and say we have a new parameterization $\mathbf{p}=\mathbf{c}\circ h$

if it is orientation preserving, otherwise multiply by -1