hey...so my problem is to rewrite the [integral from 0 to pi/2] of in terms of the elliptic integral E(k, phi) = [integral from 0 to phi] .
please note i am aware elliptic integrals are unsolvable in closed form...i am not looking for a solution, I am just attempting to rewrite the integral to make it look like the form of the elliptic integral E
using the substitution tanu = asinx, I have worked it out to be: [integral from 0 to arctan(asinx)]
but I can't figure out where to go from here. Please help!
thanks, but unfortunately I need to solve it a specific way, because I'll use the results in later problems. I've worked it down to:
subst.
so
and dx =
the integral becomes: [integral from 0 to arctan(a)]
(after a few simple steps of manipulation)
I need to finish it with this method to solve the problem, but am stuck here. Can someone please help? I have been stuck for 3 days and it's driving me crazy!!