Please verify answer to centroid of area

[MAC-A-TAC]

Hello.

Would you please verify that my answer is correct to the following problem:
Find the centroid of the area bounded by the parabola y = 4-x[sup:22wj68zu]2[/sup:22wj68zu] and the x -axis.

My solution is (0,1.6).

I am attaching my work for reference.

As always your help is greatly appreciated.

 

[Deleted member 4993]

You should use limits in your M[sub:3kyun4oh]x[/sub:3kyun4oh] calculation. The way you did it is correct for the given problem - but for many practical (civil and mechanical engineering) problems - you won't be able to use that method.

\(\displaystyle \int_{-2}^{2}\frac{1}{2}(x^4 \, - 4)^2 dx \, = \, 2\cdot [\frac{32}{10} \, - \, \frac{4\cdot 8}{3} \, + \, 8 \cdot 2] = \frac{256}{15}\)