Find the center of mass (x,y) of the region bounded by the graphs of f(x)=4-x^2 and g(x)=x+2.
Hi
First draw the curves
Then compute the intersects of the 2 curves by solving $\displaystyle 4-x^2 = x+2$
Spoiler:
The coordinates of the center of mass G are given by the formula
$\displaystyle x_G = \frac{\int\int x\:dx\:dy}{\int\int dx\:dy}$
$\displaystyle y_G = \frac{\int\int y\:dx\:dy}{\int\int dx\:dy}$
You can see that the area is defined by :
x between -2 and 1 ; y between (x+2) and 4-x² (see green line)
Therefore
Spoiler: