The correct answers are given but I don't understand how to get them. I was told that some Calculus is needed to solve this problem. Please explain and thank you for your help. Here is the problem:

Below is a picture of a rigid rod of mas and length . This is a rod of non-uniform density. It's density is

1) Find the center of mass of the rod (the correct answer should be ).
2) What is the moment of inertia of the rod about the y-axis? (the correct answer should be )

uploaded image


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