I have very hard instructor for multivariate calculus. He ask if the next integral is well-defined.
$ \iint\limits_D\,{\cos(z)\sin^3(z)\cos(y)\sin(y)\over (\cos^2(z)+\sin^2(z)\cos^2(y))(\cos^2(z)+\sin^2(z)\cos^2(y)-b)}\,dy\,dz $
$D$ is the region $[0,\pi] \times [0,\pi]$ and $b \in (0,1]$. Is it possible to calculate integral with Mathematica or by hand for all $b$? I consider this an improper integral. For $b=1$, the free version of Wolfram Alpha says that the integral is $0$, but it is not strong enough to calculate the integral for general values of $b$.