1. The problem statement, all variables and given/known data This is a very simplified physics problem, just need help with the calc part: What x value represents the average of the area for the semicircle with the equation y = +- (r^2 - x^2)^(1/2)? 2. Relevant equations I called the integral A(x) because it represents area: A(x) = +- ( (.5) ( x (r^2 - x^2)^(1/2) + r^2 arcsin (x/r) ) ) r > 0 3. The attempt at a solution I bounded the region to 0 < x < r (so it represents a semi-circle of radius r in the positive x region). A(0) = 0 A(r) = +- ( (.5) ( r (r^2 - r^2)0^(1/2) + r^2 arcsin (r/r) ) ) A(r) = +- ( (.5) ( (0) + (r^2 * 90) ) A(r) = +- (45 * r^2) Then the average formula is (I think) ( A(0) + A(r) ) / (0 + r), but when I do that my average is +- (45 * r)...which can't be right, since the average x value has to be somewhere between 0 and r Maybe you just...can't do the average for something that's split into two formulas like this? If you can't, is there any way you can?