Compute the area of the spandrel bounded by the $x$ -axis, the line $x = b$, and the curve $y = kx^n$ where $n ≥ 0$. What is the location of its centroid from the line $x = b$?

Determine also the $y$ coordinate of the centroid.

$A = \dfrac{bh}{n + 1}$

$\bar{x} = \dfrac{b}{n + 2}$

$\bar{y} = \dfrac{n + 1}{4n + 2}h$

More info.