The distances x (in in.) from one end of a barrel plug (with vertical cross section) to its center of mass, as shown in the figure is
x=0.9129 integrate x*square root of (0.3-0.1x) (0<=x<=3)
Find x with n=12
In real life, Simpson's rule is very practical and helpful to solve the curve distance. Here I give a real example how to approach this kind of problem with Simpson's rule.