Evaluate $\iint_D xy$ [closed]
$\sin(x)=\cos(x)$ when $x=\frac{\pi}{4}+k\pi$ thus your integral becomes
$$\int_{\frac{\pi}{4}}^{\frac{5}{4}\pi}x\left[\int_{\cos(x)}^{\sin(x)} y dy \right]dx$$
I think you can easy solve these integrals without difficulty. As you can see, no polars are needed.