MvCalc58

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\int _{0}^{2}\int _{1}^{z}[yz{\frac  {x^{2}}{2}}]_{{0}}^{{yz}}dydz\,

=\int _{0}^{2}\int _{1}^{z}[yz{\frac  {y^{2}z^{2}}{2}}]dydz\,

=\int _{0}^{2}[\int _{1}^{z}{\frac  {y^{3}z^{3}}{2}}dy]dz\,

=\int _{0}^{2}[z^{3}{\frac  {y^{4}}{8}}]_{1}^{z}dz\,

=\int _{0}^{2}[{\frac  {z^{7}}{8}}-{\frac  {z^{3}}{8}}]dz\,

=[{\frac  {z^{8}}{64}}-{\frac  {z^{4}}{32}}]_{0}^{2}\,

={\frac  {256}{64}}-{\frac  {16}{32}}=4-{\frac  {1}{2}}={\frac  {7}{2}}\,


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