- #1

karush

Gold Member

MHB

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$\textsf{Evaluate the triple integral}\\$

\begin{align*}\displaystyle

I_{\tiny{11}}&=\int_{0}^{\pi/6}\int_{0}^{1}\int_{-2}^{3} y\sin{z}

\, d\textbf{x} \, d\textbf{y} \, d\textbf{z}\\

&=\int_{0}^{\pi/6}\int_{0}^{1}

\Biggr|xy\sin{z} \Biggr|_{-2}^{3}

\, d\textbf{y} \, d\textbf{z}\\

ans&=\color{red}{\frac{5(2-\sqrt{3})}{4}}

\end{align*}ok just want to see if these first steps are correct with xyz