Answer
$\dfrac{65}{28}$
Work Step by Step
Consider $I=\iiint_E 6xy dV$
$I= \int_{0}^1 \int_{0}^{\sqrt x} \int_{0}^{1+x+y} 6xy dz dy dx= \int_{0}^1\int_{0}^{\sqrt x} |6xyz|_{0}^{1+x+y} dy dx$
or, $=\int_{0}^1\int_{0}^{\sqrt x} 6xy+6x^2y+6xy^2 dy dx$
or, $=\int_0^1 [3xy^2+3x^2y^2+2xy^3]_{0}^{\sqrt x}dx$
or, $= \int^{0}_{1}[3x^2+3x^3+2x^{5/2} dx$
or, $= [x^3+\dfrac{3x^4}{4}+(2)\dfrac{2}{7}x^{7/2}]^{0}_{1}$
or, $=\dfrac{65}{28}$
