Area Moment of Inertia

Subject: 
Mechanics
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THIS PROBLEM NEEDS UPDATE !!!

The definition of second moment of inertia is I= y^2 dA and not I= y^2 dx. On the FE reference handbook (p.59) it is given that Ix of half a parabola (y^2=x) is Ix=2ab^3/15 where a= width and b=height. For this problem, it would be equal to 7.45.