Double integral of delta functions I need to evaluate the following integral:
$$ \int_0^\pi \int_1^2 \delta(x^2 - y^2)\delta(\sin(x))\,\mathrm dy\,\mathrm dx$$
I tried moving the $ \delta(\sin(x)) $ out of the integral and proceeding from there. I know how to simplify $ \delta(x^2 - y^2) $, but what is confusing me is how to evaluate its integral with respect to $y$, since its value would depend on whether or not $x$ lies in the interval $(1,2)$. But $x$ is still a variable, and not a constant so I don't know what to do.
If someone could explain how to evaluate this integral it would be appreciated!

Assume the function $f(x,y) = \delta(x^2 - y^2),  x\in[0,\pi],  y \in[1,2]  $
It is only nonzero when $x=y$ or $x=-y$; since all values are positive, we only consider $x=y$. Then, you just need to evaluate the integral over the path that $x=y$ for their possible values which is $x=y \in [1,2]$. Now if you look at $\delta(sin(x))$ it is only non-zero when $x=(2k+1)\pi$, which never happens if we limit $x$ to $[1,2]$. Then the answer is zero. 
