# Limit of a centroid of area

1. Mar 25, 2013

### tinylights

1. The problem statement, all variables and given/known data
Okay, so the idea here is to take the centroid bounded by the x-axis and 1-x^n. N should be an even and positive integer. We should take the limit as n approaches infinity of both the x- and y-coords of the centroid, hopefully ending up with (0, 1/2).

2. Relevant equations
Formula for a centroid: A = integral of f(x), Mx = integral of xf(x), My = integral of f(x)^2 over 2. All of them should be definite integrals with the same "a" and "b" - I picked 0 and 1 and multiplied the whole thing by two since it appears to be an even function.

Then you divide Mx/A for your x-coord, My/A for your y-coord, and take the limit.

3. The attempt at a solution

See above. I am doing these steps over and over again but keep ending up with the same weird things. I get (n+1)/2(n+2) for my Mx/A, and this long convoluted thing for My/A - 1-2n+1/n+1 + 1/2n+1 / 2(1 - 1/n+1). This would be fine except the limit for Mx/A seems to be 1/2, when it really should be 0, and I'm certainly not getting a limit of 1/2 for My/A.