Answer
$\dfrac{3}{4}$
Work Step by Step
Total area of the triangle: $\ Area; A = \dfrac{3}{2}$
Let us consider that $Volume =\int_0^1 \int_0^{3x} x \ y \ dy \ dx \\=\dfrac{1}{2} \times \int_0^1 x [y^2]_0^{3x} dx \\=\dfrac{9}{2} \times \int_0^1 x^3 dx \\=\dfrac{9}{8} [ x^3]_0^1 dx \\ =\dfrac{9}{8}$
Now, the average volume becomes:
$V_{Av}= \dfrac{Total \ Volume}{Total \ Area}=\dfrac{9/8}{3/2} =\dfrac{3}{4}$