I am trying to find the centroid ($\bar{x}, \bar{y}$) of the region bounded by the curves: $$y = x^3−x$$ and $$y = x^2 − 1$$
I've tried this a few times and can't get to the correct answer. I feel like I'm missing something, like I have to account for an offset perhaps.
So far I've gotten $A = 4/3$ by integrating $\int_{-1}^1 (f(x)-g(x)) dx$.
The limits of integration from $-1$ to $1$, based on a graph of the 2 functions.
$\bar{x} = 4/5$ via $$\frac{1}{A} \int_{-1}^1 (x(f(x)-g(x))dx,$$ and $\bar{y} = -12/35$ via $$\frac{1}{A} \int_{-1}^1 \frac{1}{2}(f(x)^2-g(x)^2)dx$$
This is a homework question but it's only worth one point and I've finished the rest so I'm more asking out of wanting to know what I've done wrong. I've had a few almost identical questions that I had no problem with.