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:
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?
OK, so I figured out what I was doing wrong. I was apparently supposed to use Line Integrals to solve this problem instead of a double integral. Double integrals solve for a solid lamina with region D. The wire does not represent a lamina. The equation I would use is:
after converting to parametric equations.
In case anyone encounters a similar question.