Answer
$\frac{1}{4}$
Work Step by Step
$\int_{0}^{1}\int_{0}^{y}\int_{x}^{1}6xyzdzdxdy=\int_{0}^{1}\int_{0}^{y}xy[3z^{2}]|_{x}^{1}dxdy$
$=\int_{0}^{1}\int_{0}^{y}xy[3-3x^{2}]dxdy$
$=\int_{0}^{1}\int_{0}^{y}[3xy-3x^{3}y]dxdy$
$=\frac{3y^{4}}{8}-\frac{3y^{6}}{24}|_{0}^{1}$
$=\frac{3}{8}-\frac{1}{8}$
$=\frac{1}{4}$
