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

The center of mass of a two-dimensional region surrounded by $y=f(x)$ and $y=0$ is the point $({\bar {x}},{\bar {y}})$ given by

${\bar {x}}={\frac {1}{A}}\int _{a}^{b}xf(x)\,dx$

${\bar {y}}={\frac {1}{2A}}\int _{a}^{b}(f(x))^{2}\,dx$

where $A$ is the area of the region and a and b are the points where the function crosses the x-axis.