MvCalc44

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The moment of inertia in the first quadrant,I_{x}=I_{y}={\frac  {1}{2}}I_{0}={\frac  {1}{2}}\iint _{R}(x^{2}+y^{2})dxdy\,

={\frac  {1}{2}}\int _{{0}}^{{{\frac  {\pi }{2}}}}\int _{0}^{a}(r^{2})rdrd\theta \,

={\frac  {1}{2}}{\frac  {a^{4}}{4}}{\frac  {\pi }{2}}\,

={\frac  {1}{16}}\pi a^{4}\,

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