Answer
$\frac{81}{2}$
Work Step by Step
$\int\int_{E}xydV=\int_{0}^{3}\int_{0} ^{x}\int_{0} ^{x+y} xydzdydx$
$=\int_{0}^{3}\int_{0} ^{x} xyz|_{0} ^{x+y}dydx$
$=\int_{0}^{3}\int_{0} ^{x} x^{2}y+xy^{2}dydx$
$=\int_{0}^{3}\frac{ x^{2}y^{2}}{2}+\frac{xy^{3}}{3}|_{0} ^{x}dx$
$=\int_{0}^{3}\frac{ 5x^{4}}{6}dx$
$=[\frac{ x^{5}}{6}]|_{0}^{3}$
$=\frac{81}{2}$
