In solving an integral of sqrt(9-x^{2}), we substitute x=3sin(t) to get an integral of 3cos(t). Why does this work? In the original function, x can take on any value(if you include imaginary numbers), but the new function is equivalent to the original one even though sin(t) takes values only between its amplitudes.

P.S. I remember a guide to writing math in this forum. Anyone have the link?

**Edited by DylsexicChciken, 12 September 2014 - 03:35 AM.**