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] SQRT(1-(ksinx)^2)dx

F(k,y) = [integral from 0 to y] dx/SQRT(1-(ksinx)^2)

II(k,y) = [integral from 0 to y] dx/((1+n(sinx)^2)SQRT(1-(ksinx)^2))

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 = 1/SQRT(1-v^2) * dv

so E becomes: [integral from 0 to siny] SQRT(1 - (kv)^2)/SQRT(1-v^2) * dv
and I don't know what to do from there...