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\textbf{Multiple Integration}

\textit{\textbf{Iteration of Double Integrals}}
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\textbf{Question}

Sketch the domain of integration, and calculate the iterated integral
for
$$\int_0^{\pi/2} \,dy \int_y^{\pi/2} \frac{\sin x}{x} \,dx$$


\textbf{Answer}

$$ \ $$
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\begin{eqnarray*}
I & = & \int_0^{\pi/2} \,dy \int_y^{\pi/2} \frac{\sin x}{x} \,dx\\
& = & \int\!\!\!\int_T \frac{\sin x}{x} \,dA\\
& = & \int_0^{\pi/2} \frac{\sin x}{x} \int_0^x \,dy\\
& = & \int_0^{\pi/2} \sin x \,dx =1
\end{eqnarray*}

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