
tough trig substitution
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] $\displaystyle SQRT(1(ksinx)^2)dx$
F(k,y) = [integral from 0 to y] $\displaystyle dx/SQRT(1(ksinx)^2)$
II(k,y) = [integral from 0 to y] $\displaystyle dx/((1+n(sinx)^2)SQRT(1(ksinx)^2))$
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 = $\displaystyle 1/SQRT(1v^2) * dv$
so E becomes: [integral from 0 to siny] $\displaystyle SQRT(1  (kv)^2)/SQRT(1v^2) * dv$
and I don't know what to do from there...