3. Let $\Omega=\{(x,y)\mid x^2+y^2\le 1\}$. Given

$$A=\iint_\Omega \sin(x^2)\cos(y^2)\,dx\,dy$$ $$B=\iint_\Omega \cos(x^2)\sin(y^2)\,dx\,dy.$$

Let $C=A+B$. Then $C$ is equal to an iterated integral which is expressed in terms of polar coordinates $r$ and $\theta$.

i) $(10\%)$ First derive this iterated integral expression for $C$ in polar coordinates, then compute the value of $C$.

ii) $(10\%)$ Prove that $A=B$.