# Average Value - Ellipse

1. Aug 11, 2011

### IHave

1. The problem statement, all variables and given/known data
Find the average value of the positive y-coordinates of the ellipse x^2/a^2 + y^2/b^2 = 1

"Average" means to sum the numbers in a set and divide by how many you added; i.e. ${\Sigma x_n} \over {n}$. Since the ellipse has a continuous nature, to "sum" the y-coordinates means to integrate over an interval. The "number of addends" here is the length of the interval, so we divide by that.
$${{1} \over {2a}}{\int^a_{-a} \sqrt{b^2 (1 - {x^2 \over a^2})} \quad dx}$$