<s>[INST] Help with Evaluating triple integral Evaluate $\int \int \int_B xyz^2 dV$, where B is a cuboid bounded by the regions $ 0 \le x \le 1 $, $ -1 \le y \le 2 $, $ 0 \le z \le 3 $. 
I keep getting $ \frac{27}{4}$ as my answer but apparently it's incorrect...Any help would be appreciated.
 [/INST] This is equivalent to
\begin{align*}
\int_0^1 x dx \int_{-1}^2 y dy \int_0^3 z^2 dz &= \left(\frac{1}{2} x^2 \Big|_0^1\right) \left(\frac 1 2 y^2\Big|_{-1}^2\right) \left(\frac 1 3 z^3 \Big|_0^3 \right) \\
&= \frac{1}{2} \cdot \left(\frac{4}{2} - \frac{1}{2}\right)\cdot \frac{3^3}{3} \\
&= \frac{1}{2} \cdot \frac{3}{2} \cdot 9 \\
&= \frac{27}{4}
\end{align*}
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