Question

compute using polar coordinates to show this integral equals pi

{double integral} e^-(x^2+y^2) dx dy, x=-inf..inf, y=-inf..inf

Answer 1

http://www.wolframalpha.com/input/?i=integrate+e^-%28x^2%2By^2%29+dx+dy%2C+x%3D-inf..inf%2C+y%3D-inf..inf

Answer 2

\[x^2+y^2=\rho^2\quad,\quad dxdy=\rho d\rho d\phi\quad;\quad \rho\in[0,+\infty)\quad,\quad\phi\in[0,2\pi]\]