polar coordinate

**user** · April 5th 2010, 07:20 AM

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 $

**dwsmith** · April 5th 2010, 09:30 AM

$x^2+y^2=r^2$

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

**elim** · April 5th 2010, 09:32 AM

$ \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 $

Thread: polar coordinate

LinkBack

Thread Tools

Display

polar coordinate

Similar Math Help Forum Discussions

[SOLVED] HowTo:upper and lowerlimit of integral from Cartesian coordinate to polar coordinate?

Polar coordinate

polar coordinate

Polar Coordinate..

Polar Coordinate 03

Search Tags