How do i solve this double integral $$\int_0^1\int_{-\pi}^\pi x\sqrt{1-x^2\sin^2(y)}\mathrm{d}y\mathrm{d}x$$
How do I solve this question here? 

Integrate with respect to $y$ first $\displaystyle \int_0^1 \left (\int_{-\pi}^\pi x\sqrt{1-x^2sin^2(y)}dy\right)dx$, This $\displaystyle \int_{-\pi}^\pi x\sqrt{1-x^2sin^2(y)}d y = f(x)$  will give you a function $f(x)$, then you can compute $\displaystyle \int_0^1f(x)dx$.
