Answer
$\dfrac{3e-7}{6}$
Work Step by Step
Consider $I=\iiint_E e^{z/y} dV$
$ I=\int_{0}^1 \int_{y}^{1} \int_{0}^{xy}e^{z/y} dz dx dy= \int_{0}^{1} \int_{y}^{1} [ye^{z/y}]_{0}^{xy} dx dy$
or, $=\int_{0}^1 [ye^{x}-xy]_y^1 dy$
or, $= \int_{0}^{3} [yx+y^2-yx+y^2] dy dx$
or, $= \int_0^{1}[(e-1)y-ye^y+y^2] dy$
or, $=[(e-1)(1/2)y^2-(ye^y-e^y) +\dfrac{1}{3}y^3]_0^1$
or, $=\dfrac{(e-1)}{2}-e+e+\dfrac{1}{3}-1$
or, $=\dfrac{3e-7}{6}$
