Here is a link to a pdf .http://www.mrskeller.net/documents/hwsols14.pdf
I'm having issues with number 56. The solution makes no sense to me.
The Attempt at a Solution
So, I did graph the equation y = sqrt(r^2 - x^2) and I understand that height of the circle. I understand that you need to integrate from -r to r. But I do not understand the integral by any means.
They have ##\int 4(r^2-x^2)) dx ## from -r to r
I thought that maybe there were doing something of the form ∏∫y^2 because that is what this chapter uses. But I guess not. They say that the length of a side is 2y = 2sqrt(r^2 - x^2). And the only way that I can see how to get from that equation to the integral they suggest is ly squaring 2y = 2sqrt(r^2 - x^2). So I don't understand that even because if you squared it and used the integral of the form ∏∫y^2 dx then your 4 dissapears. I just don't understand what is going on with this problem. Thanks