12. use the substitution v = sinx to write the elliptic integrals F(k,y),
E(k,y), and II(k,y) in terms of k and u = siny
where E(k,y) = [integral from 0 to y]
F(k,y) = [integral from 0 to y]
II(k,y) = [integral from 0 to y]
where, for all of them, 0 < k < 1, and 0 <= y <= pi/2
I do the substitutions but get stuck at each one, for example with E(k,y):
1. subst v = sinx
i.e. x = arcsinv
dx =
so E becomes: [integral from 0 to siny]
and I don't know what to do from there...