The question is related to Buffon's needle experiment: I was wondering how to change the order of integration. The integral is shown below. Apologies if I have left out lots of stuff, I'm quite new to this level of mathematics.
$$\int_{\theta=0}^{\frac{\pi}{2}} \int_{b=0}^{\frac{l}{2} \cdot \sin (\theta)} \frac{4}{\pi d} \cdot d b \cdot d \theta=\frac{2 \cdot l}{\pi \cdot d}$$