Evaluate the triple integral of sin2z/(4-z) dydzdx where the limits of integration for outer limits (x) are from 0 to 2, the middle limits (z) are 0 to 4-(x^2), and the inner limits (y) are 0 to x.
The Attempt at a Solution
I'm not sure what the best approach is for this integral. Should I start by tackling the hardest one (dz), or work on the dx and dy integrals where the integrand is a constant? My attempt at the problem involved integrating wrt x first, then wrt y. I got the integral of 2xsin2z/(4-z) dz, from 0 to 4-x^2. I guess what's throwing me off is that trig function. Only thing I can think of is by parts...
Edit: Integrated wrt y then wrt x, got 2sin2z/4-z, so that's a bit simpler. Still need to integrate wrt z. I'm thinking by parts but wondering if there's a more efficient way that I might be missing.