I need to find the radon transform of the following function. But I got stuck in finding this integral. Let $\chi$ be given by
$$\chi(t) = \begin{cases} 1 & |t|< 1/2 \\ 0 & \text{otherwise}\end{cases}$$
Then Radon transform would be obtained by this integral.
$$\int_{s_A}^{s_B}\chi(\rho -s\alpha)\chi(\rho^{'} +s \beta)\,ds$$
where $$s_A,s_B$$ are two numbers.
I have the answer for this and I am supposed to check it to see if it is right or not but each time I end up with a different answer. Could you please give me a brief hint on calculation of this integral?