Answer
$\dfrac{1}{4} $
Work Step by Step
Consider $Average=\int_{0}^{1} \int_{0}^{1} xy \ dy \ dx$
or, $=\int_{0}^{1} [\dfrac{xy^2}{2}]_0^1 \ dx$
or, $=\int_{0}^{1} \dfrac{x}{2} \ dx$
or, $=\dfrac{1}{2} \times \int_{0}^{1} x \ dx$
or, $=\dfrac{1}{2} [\dfrac{x^2}{2}]_0^1$
or, $=\dfrac{1}{4} \times (1-0) $
or, $=\dfrac{1}{4} $
