Question:

A wire takes the shape of the semicircle y= . Find the center of mass of the wire if the linear density at any point is proportional to its distance from the line .

So far I have this:

The Double Integral I have is:

with

Which works out to

I then attempt to solve the expression:

I end up with the answer of:

whereas the correct answer is:

Any ideas where I went wrong?

Thanks,

Mike