§15.8 Substitutions in Multiple Integrals

(see also last two videos of §15.7)

Lecture notes

Jacobians and substitution

Examples

  1. Find $\displaystyle\int_1^3 \int_{1/y}^y \sqrt{\frac yx}e^{\sqrt{xy}}\,dx\,dy.$
  2. Find $\displaystyle\int_0^\pi\int_0^{2y}\cos(x-2y)(x+y)\,dx\,dy.$