Volume of an n-sphere

As i mentioned earlier, I am trying to estimate the volume of an n-sphere, both using the normal newton-cotes methods of integration and using the monte carlo integration methods. I finally figured out how to do measure the volume of a 2 sphere or a sphere in 3 dimensions. I was being stupid and I hadn't put enough thought into the problem, which was evident in the amount of time I wasted implementing faulty methods and second guessing coincidentally approximate results. Moving on to higher dim spheres now!

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