MvCalc35

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Area A=\iint _{D}dxdy\, where D is the region with the limits of x varying from 0 to 1 and y from x^{{{\frac  {2}{3}}}}\, to x^{{{\frac  {3}{2}}}}\,

Thus A=\int _{0}^{1}\int _{{x^{{{\frac  {3}{2}}}}}}^{{x^{{{\frac  {2}{3}}}}}}dydx\,

=\int _{0}^{1}(x^{{{\frac  {2}{3}}}}-x^{{{\frac  {3}{2}}}})dx\,

=[{\frac  {3}{5}}x^{{{\frac  {5}{3}}}}-{\frac  {2}{5}}x^{{{\frac  {5}{2}}}}]_{0}^{1}\,

={\frac  {3}{5}}-{\frac  {2}{5}}={\frac  {1}{5}}\,


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