Answer
$9(e-1)$
Work Step by Step
The region of integration can be expressed as: $R=${$ (x,y) | 0 \leq x \leq 1/y, 1 \leq y \leq 10$}
Consider $I=\int_{1}^{10} \int_{0}^{1/y} ye^{xy} \ dx \ dy$
or, $=\int_{1}^{10} [e^{xy}]_{0}^{1/y} \ dy$
or, $=\int_{1}^{10} (e-1) \ dy$
or, $=[(e-1)y]_{1}^{10}$
or, $=10(e-1)-(e-1)$
or, $=9(e-1)$
