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teleport

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Give the moment of inertia for a rhombus with sides of length c and mass m, about an axis that is parallel to the plane of the rhombus and goes from one corner to the opposite corner.

I have set up the integral:

I=(m/c^2)*2* int(from x=0 to x=c) int(from y=x to y=-x+c*sqrt2)x^2dydx.

where I have used the y-axis as the axis of rotation.

I don't know if this is the correct integral. In particular I suspect of the 2 multiplying the first integral. The thing is that this 2 would be correct if I were just finding the area of the rhombus, but since i have introduced the

x^2 that doesn't have anything to do with the area, then I don't know if it works here.