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 ${\bar {y}}={\frac {1}{A}}\int _{a}^{b}\left[{\frac {f(x)+g(x)}{2}}\right][f(x)-g(x)]\;dx,$ where $A$ is the area of the region (this formula can be found in the CLP-2 Integral Calculus textbook).