Answer
$\dfrac{5}{8}$
Work Step by Step
Here, we have
$ \int_{0}^1 \int_{x}^{2x} \int_{0}^{y} 2xyz dz dx dy= \int_{0}^1 \int_{x}^{2x} |xyz^2|_{0}^{y} dx dy$
or, $=\int_{0}^1\int_x^{2x} xy^3 dy dx$
$=\int^{0}_{1}(\dfrac{xy^4}{4}]_x^{2x}dx$
or, $=\dfrac{15}{4}\int_0^1 x^5 dx$
or, $=[\dfrac{15}{4}(x^6/6)]_0^1$
or, $=\dfrac{5}{8}$