## Calculus 8th Edition

$\frac {41}{24}$
Since, $D=(x,y) | 0\leq y\leq 1, y^{2}\leq x \leq y+2$ $\int\int_{D} xydA=\int_{0}^{1}\int_{y^{2}} ^{y+2}xydxdy$ $=\int_{0}^{1}[\frac{x^{2}}{y}]_{y^{2}} ^{y+2}dxdy$ $=(\frac {y^{4}}{8}+\frac{2}{3}y^{3}+y^{2}-\frac{y^{6}}{12}]_{0} ^{1}$ $=\frac{1}{8}+\frac{2}{3}+1-\frac{1}{12}$ $=\frac {41}{24}$