MvCalc23

From Example Problems
Jump to: navigation, search

The region is x=1 to 2 and y is from 0 to {\frac  {1}{x}}\,

Now the given integral is \iint _{R}xydxdy=\int _{1}^{2}[\int _{{y=0}}^{{{\frac  {1}{x}}}}xydy]dx\,

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

=\int _{1}^{2}[x{\frac  {1}{x^{2}}}]dx\,

=\int _{1}^{2}{\frac  {dx}{x}}=[\log x]_{1}^{2}=\log 2-\log 1=log2\,


Main Page