# tough trig substitution

• September 28th 2008, 03:34 PM
minivan15
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] $SQRT(1-(ksinx)^2)dx$

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...