MvCalc54

From Example Problems
Jump to: navigation, search

First integrating with respect to z,we get

\int _{0}^{1}\int _{0}^{x}[(x+y)z+{\frac  {z^{2}}{2}}]_{{0}}^{{x+y}}dydx\,

={\frac  {3}{2}}\int _{0}^{1}\int _{0}^{x}(x+y)^{2}dydx\,

={\frac  {3}{2}}\int _{0}^{1}\int _{0}^{x}(x^{2}+y^{2}+2xy)dydx\,

={\frac  {3}{2}}\int _{0}^{1}[x^{2}y+{\frac  {y^{3}}{3}}+xy^{2}]_{0}^{x}dx\,

={\frac  {7}{2}}\int _{0}^{1}x^{3}dx\,

={\frac  {7}{2}}[{\frac  {x^{4}}{4}}]_{0}^{1}={\frac  {7}{8}}\,

Main Page