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# Moment of Inertia - multiple integration Watch

1. Hello, could I please have some help with the second part of this question please?

Consider a two-dimensional elliptical rigid body in the xy plane, the circumference of which is described by where a and b are positive constants. The mass per unit area is given by,

Show that the total mass is given by which I can do - fairly straightforward surface integral.

The next part is show that the moment of inertia wrt the x axis is,

I said that I_x was the integral of y^2 dm, which is,

. Can someone point out my mistake please? I.e. is it a mistake in setting up the problem or in carrying out the integration?

2. (Original post by KeyFingot)
I said that I_x was the integral of y^2 dm, which is,

. Can someone point out my mistake please? I.e. is it a mistake in setting up the problem or in carrying out the integration?

Why have you replaced with the limit in the initial integral? It varies between 0 and that.
3. (Original post by ghostwalker)
Why have you replaced with the limit in the initial integral? It varies between 0 and that.
because I'm being very foolish haha! I somehow thought I had to remove the y dependence from the integral :s. Thanks once again for your help

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