benhou

I was trying to derive the formula for the moment of inertia of a rectangular prism at its centre of mass. And ended up with this:

[tex]\frac{1}{2}M(a/2)^{2}+2\frac{M}{ab}\int^{b/2}_{a/2}arccos(\frac{a^{2}}{2r^{2}}-1)rdr+4\frac{M}{ab}\int^{\sqrt{a^{2}+b^{2}}}_{b/2}(\frac{\pi}{2}-arccos\frac{b/2}{r}-arccos\frac{a/2}{r})rdr[/tex]

Due to the limitation of my knowledge in Calculus, I was stuck here. Can anyone help me solve these two integral:

[tex]\int arccos(\frac{a^{2}}{2r^{2}}-1)rdr[/tex]

[tex]\int (\frac{\pi}{2}-arccos\frac{b/2}{r}-arccos\frac{a/2}{r})rdr[/tex]