Question

Integrate the function. I think it would be better to change to polar coordinates.

Answer 1

\[\int\limits_{0}^{1}\int\limits_{-\sqrt{1-x^2}}^{\sqrt{1-x^2}} e^{-(x^2+y^2)} dydx\]

Answer 2

whoa wow

Answer 3

thanks...

Answer 4

why would you want to change it

Answer 5

take the partial derivative with respects to y and then do the first integral

Answer 6

\[\int\limits_{0}^{1}\int\limits_{-\sqrt{1-x^{2}}}^{\sqrt{1-x^{2}}}e^{-(x^{2}+y^{2})}dydx=\int\limits_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\int\limits_{0}^{1}e^{-r^2}rdrd \theta=\frac{(1-e^{-1})\pi}{2}\]