Evaluate the triple integral. $$ \iiint_{G} x y z d V $$ where $$ G $$ is the solid in the first octant that is bounded by the parabolic cylinder $$ z=3-x^{2} $$ and the planes $$ z=0, y=x $$ and $$ y=0 $$.

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Rojas Dunn · Accepted Answer

The value of the triple integral is $$ \frac{27}{32} $$.

Evaluate the triple integral. \[ \iiint_{G} x y z d V \] where \( G \) is the solid in the first octant that is bounded by the parabolic cylinder \( z=3-x^{2} \) and the planes \( z=0, y=x \) and \( y=0 \).

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Evaluate the triple integral. \[ \iiint_{G} x y z d V \] where \( G \) is the solid in the first octant that is bounded by the parabolic cylinder \( z=3-x^{2} \) and the planes \( z=0, y=x \) and \( y=0 \).

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