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