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...