Answer
See explanation below.
Work Step by Step
a) We can say that the center of mass is where we can balance a plate.
b) If $(x_1,y_1) $is the center,
$$x_1= 1/A *\int_{a}^{b} x*f(x) dx$$ and $$y_1 = 1/A * \int_a^b 1/2 * (f(x))^2$$
Where A is the integral of $f(x)$ from $a$ to $b$
