Question

Computing area under whole normal distribution function.

Answer 1

\[\int\limits_{-\infty}^{+\infty}e^{-x^2}dx = \sqrt{\int\limits_{-\infty}^{+\infty}\int\limits_{-\infty}^{+\infty}e^{-x^2-y^2}dxdy} = \sqrt{ \int\limits_{0}^{2\pi}\int\limits_{0}^{\infty} r e^{-r^2}drd \theta }\]
The integral is further evaluated, but my question is - the transformation of cartezian to polar coords, I got the (x^2 + y^2)=r^2 part, but I cannot see why the diameter appears in front of the exponetial. Any ideas?

Multivariable transformation of coords - please only uni-level answers, thanks.

Answer 2

@zarkon he seems to be a sevant at these things.

Answer 3

If you have time, see
http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-17-polar-coordinates/

Answer 4

and for more details on your problem
https://www.youtube.com/watch?v=fWOGfzC3IeY

Answer 5

what diameter?

Answer 6

you mean why x^2+y^2=r^2?