I am looking for feedback on some points actually. I am looking at the centroid equation $\frac{\int x f(x) dx}{\int f(x) dx}$, assuming that the integrals are bounded, will not consider constants.
I was trying to see if I can simplify this a little bit by considering opening the numerator by parts.
So one version of the numerator would be $$x \int f(x) dx - \int\int f(x) dx dx$$
other $$\frac{1}{2}\left(x^2 f(x) - f'(x) + f''(x)+ \dots \right)$$
Any idea is this can be simplified