Science:Math Exam Resources/Courses/MATH101/April 2015/Question 08 (b)/Hint 1

The center of mass of a two-dimensional region surrounded by ${\displaystyle y=f(x)}$ and ${\displaystyle y=0}$ is the point ${\displaystyle ({\bar {x}},{\bar {y}})}$ given by
${\displaystyle {\bar {x}}={\frac {1}{A}}\int _{a}^{b}xf(x)\,dx}$
${\displaystyle {\bar {y}}={\frac {1}{2A}}\int _{a}^{b}(f(x))^{2}\,dx}$
where ${\displaystyle A}$ is the area of the region and a and b are the points where the function crosses the x-axis.