# polar coordinate

• April 5th 2010, 08:20 AM
user
polar coordinate
Hi please, can you help me to solve this integral using polar coordinate
Thank you

$
\int_{-\infty}^{\infty}\int_{-\infty}^{\infty} e^{-(x^2+y^2)}dxdy
$
• April 5th 2010, 10:30 AM
dwsmith
$x^2+y^2=r^2$

Now you have $e^{-r^2}$ which is the same as doing polar since you have $x=rcos and y=rsin$ and squaring both removes the trig
• April 5th 2010, 10:32 AM
elim
$
\int_{-\infty}^{\infty}\int_{-\infty}^{\infty} e^{-(x^2+y^2)}dxdy=\int_{0}^{\infty} \int_{0}^{2\pi} e^{-r^2}r d \theta dr = 2\pi \int_0^{\infty} e^{-r^2}r dr = \pi [e^{-r^2}]_0^{\infty} = \pi

$