MvCalc32

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I=\int _{0}^{a}\int _{{y=0}}^{{{\frac  {b}{a}}{\sqrt  {a^{2}-x^{2}}}}}x^{3}ydydx\,

=\int _{0}^{a}[{\frac  {x^{3}y^{2}}{2}}]_{{y=0}}^{{{\frac  {b}{a}}{\sqrt  {a^{2}-x^{2}}}}}dx\,

={\frac  {b^{2}}{2a^{2}}}\int _{0}^{a}(a^{2}x^{3}-x^{5})dx\,

={\frac  {b^{2}}{2a^{2}}}[{\frac  {a^{2}x^{4}}{4}}-{\frac  {x^{6}}{6}}]_{0}^{a}={\frac  {b^{2}a^{4}}{24}}\,


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