If we define the elliptic integral of the second kind as:
and we can write (using half-angle formula, then sub ):
then:
hey..we are studying elliptic integrals in my class and I did some additional research online....where i came across the formula for the integral of SQRT(cosx) = 2E (1/2 *x, SQRT(2)). I couldn't figure out how to get there myself...would someone mind writing out the proof of this?