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Limits of iterated integrals (parallel axis theorem)

Prim is primitive!

In genral the moment of inertia around an axis( a line) L is:
Isubl=double prim (dist(.,L)^2*delta*dA)

The collection of lines parallel to the y axis have the form x=a .Let I=Isub(y) be the usual moment of inertia around the y axis
I= double prim of x^2*delta*dA

Let I(bar) be the moment of inertia around the axis x=x(bar), where (x(bar),y(bar) is the center of mass.

Show that
I=I(bar) + M*(x(bar))^2

This is known as the parallel axis theorem

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