Determine the coordinates of the centroid of the parabolic spandrel bounded by the function $y(x) = b + kx^2$, and the lines $x =a$ and $y=b$ in terms of constants $a$ and $b$.
![diagram](./images/HW1040-above-parabola.png)
Determine the coordinates of the centroid of the parabolic spandrel bounded by the function $y(x) = b + kx^2$, and the lines $x =a$ and $y=b$ in terms of constants $a$ and $b$.