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## Homework Statement

Find the centroid of the shape formed by the equation y

^{2}=x

^{3}-x

^{4}, the x-axis, and the y-axis.

## Homework Equations

A=∫f(x)dx

Mx=∫(1/2)[f(x)]

^{2}dx

My=∫x[f(x)]dx

## The Attempt at a Solution

I'm stuck on the integral.

I attempted u-substitution and got du=(1/2)(x

^{3}-x

^{4})

^{-1/2}dx; "parts," trigonometric substitution/identities, and partial fractions don't seem to apply.