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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
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)
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