Science:Math Exam Resources/Courses/MATH101/April 2018/Question 11 (ii)/Hint 1

For the region below a curve $y=f(x)$ and above a curve $y=g(x)$ on the interval $[a,b]$, the $y$-coordinate of the centroid is given by $\overline{y}=\frac{1}{A}\underset{a}{\overset{b}{\int }}\left[\frac{f(x)+g(x)}{2}\right][f(x)-g(x)]dx,$ where $A$ is the area of the region (this formula can be found in the CLP-2 Integral Calculus textbook).