Answer
$\dfrac{27}{2}$
Work Step by Step
Consider $I=\iiint_E y dV$
$ I=\int_{0}^3 \int_{0}^{x} \int_{x-y}^{x+y} dz dy dx= \int_{0}^3 \int_{0}^{x} [yz]_{x-y}^{x+y} dy dx$
or, $=\int_{0}^1 \int_{0}^{1} [xye^{2-x^2-y^2}-xye^0] dy dx$
or, $= \int_{0}^{3} [yx+y^2-yx+y^2] dy dx$
or, $= \int_0^3(2/3) y^3|_0^x$
or, $=[\dfrac{2x^4}{1}|_0^3$
or, $=\dfrac{27}{2}$
