I was trying to solve $$ \int \int \frac{\sin \sqrt{x^2+y^2}}{\sqrt{x^2+y^2} (\frac{\pi}{2}-\sqrt{x^2+y^2})} \ \text{d}x \text{d}y$$On the domain $0 \le \theta \le \pi/2$ and $0 \le r \le \theta$.
I changed it to $$\int_{0}^{\pi/2} \int_{0}^{\theta} \frac{\sin r}{\frac{\pi}{2}-r} \ \text{d}r \text{d}\theta$$ in polar coordinates. I want to change the order here! Is it possible?
$$\int_{0}^{\pi/2} \int_{0}^{\theta} \frac{\sin r}{\frac{\pi}{2}-r} \ \text{d}r \text{d}\theta=\int_{0}^{\pi/2} \int_{r}^{\pi/2} \frac{\sin r}{\frac{\pi}{2}-r} \ \text{d}\theta \text{d}r.$$