I'm being asked to find a value at one specific point, pi, what would be my limits? All the instruction say is "what is the probability in the volume element d(phi) at phi = pi. I used the limit 0 to pi, but that is not specifically at pi.
Thats good! Use that.
but isn't that the range from 0 up to pi, and not specifically at pi? I'm not sure.
To find the probability in the volume element at phi = pi, you need to integrate the probability density over a range that includes phi = pi. In this case, since you are asked to find the probability specifically at phi = pi, the limits of integration would be from pi to pi.
However, integrating over a range of zero width will always yield zero, because you are essentially summing infinitesimally small values. Therefore, if you use the limits of integration as 0 to pi, you would not get the desired result.
Instead, you should use a different approach. Since you are looking for the probability at a specific point, you can use the PDF (probability density function) for the variable to directly evaluate the probability at that point.
Without further information about the specific probability distribution, it is difficult to provide a precise method to obtain the probability at phi = pi. Typically, you would need the functional form of the PDF or relevant equations related to the problem at hand.