Hi. In Calc 2 I have some homework questions for calculating the moments and center of mass for planar laminae. Fortunately, the book gives the exact equations necessary for the calculations, when there are functions f(x) and g(x), within bounds a and b:

$\displaystyle M_{x} = \rho\int_a^b\frac{f(x)+g(x)}{2}[f(x)-g(x)]\,dx$

$\displaystyle M_{y} = \rho\int_a^b{x[f(x)-g(x)]\,dx}$

$\displaystyle m = \rho\int_a^b{[f(x)-g(x)]\,dx}$

$\displaystyle \overline{x} = \frac{M_{y}}{m}$

$\displaystyle \overline{y} = \frac{M_{x}}{m}$

However, how do I adjust these formulae when the functions must be functions in respect to y? For example, I have a problem where the area is bounded by

$\displaystyle x = y + 2$

$\displaystyle x = y^2$

Which involves a sideways parabola.