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Math Help - centroid of region

  1. #1
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    centroid of region

    I just got back from my calculus midterm, and there was one question that I'm not sure if I got correct...

    What is the center of the region bound by y=x^2 and y=sqrt_x on 0<x<1

    When I did the math I came up with (9/20, 9/20), but intuitively I thought it would be (1/2, 1/2).

    I tried searching google because it seems like a cookie-cutter question, but didn't have much luck. I'm just wondering if I got it right.

    Thanks!
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  2. #2
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    (9/20, 9/20) is correct. The region is obviously symmetric about the line y = x, but it's not symmetric about the perpendicular line x+y = 1. In fact, it is a lens-shaped region that is fatter towards the (0,0)-end than towards the (1,1)-end.
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