Find out the center of mass for the region bounded by y = 2sin (2x), y =0 on  the interval  [0 , Π/2]

Solution

Here is a sketch (diagram) of the region along with the center of mass denoted with a dot.

Let us first obtain the area of the region.

A = ∫^Π/2₀ 2sin (2x) dx

= -cos (2x)| ^Π/2₀

= 2

 Here now, the moments (without density as it will just drop out) are,

The coordinates of the center of mass are then,

X‾ = Π/2 / 2

= Π/4

Y‾ = (Π/2)/ 2

= Π/4

Once Again, note that we didn't put in the density as it will cancel out.

 Thus, the center of mass for this region is as follow:

(Π/4, Π/4)