Question

Find the area of the region that is bounded by the given curve and lies in the specified sector.
r = e^−θ/12, π/2 ≤ θ ≤ π

Answer 1

here you have to go in polar cordinates, so you have to compute this integral:
\[\iint {r\;dr\;d\theta }\]

Answer 2

How do I do that?

Answer 3

here are your steps:
\[\iint {r\;dr\;d\theta } = \int_{\pi /2}^\pi {d\theta } \int_0^\rho {r\;dr} \]
where \(\rho = e^{-\pi/12}\)

Answer 4

oops..where \(\rho = e^{ - \theta /12} \)

Answer 5

I got this result:
\[\huge \begin{gathered}
\iint {r\;dr\;d\theta } = \int_{\pi /2}^\pi {d\theta } \int_0^\rho {r\;dr} = \hfill \\
\hfill \\
= 3\frac{{{e^{\pi /12}} - 1}}{{{e^{\pi /6}}}} \hfill \\
\end{gathered} \]