Answer
$\overline{x}=\dfrac{1}{M} \int_a^b \delta(x) [f(x)-g(x)] \ dx$ and $\overline{y}=\dfrac{1}{M} \int_a^b \dfrac{\delta}{2} [f^2(x)-g^2(x)] \ dx$
Work Step by Step
Let $\overline{x}$ and $\overline{y}$ be the center of mass of a thin plate bounded by two curves $y=f(x)$ and $y=g(x)$ over an interval $[a,b]$. This can be mathematically expressed as:
$\overline{x}=\dfrac{1}{M} \int_a^b \delta(x) [f(x)-g(x)] \ dx$ and $\overline{y}=\dfrac{1}{M} \int_a^b \dfrac{\delta}{2} [f^2(x)-g^2(x)] \ dx$
