15.3.53 Sketch the region of the double integration and evaluate

[karush]

$\textsf{a. Sketch the region of integration and evaluate.}\\$
\begin{align*}\displaystyle
\int_{6}^{\frac{\pi}{6}}
\int_{0}^{\sec{\theta}}
6r^{3} drd\theta\\
W|A=\frac{5}{3\sqrt{3}}
\end{align*}
OK I really didn't know how to do this in desmos

 

[HallsofIvy]

So your question is just about how to graph this using "Desmos"? First, to get to polar coordinates, click on the "wrench" icon in the upper right of the page, just below the menu bar. That opens a dialog box that has "Grid", "Axis Numbers", "X-Axis", and "Y-Axis" checked. Right below "Grid" are two circles, one with a rectangular pattern, the other with radii and circles. Click on the second to get a polar coordinate grid. There is no way to graph $$\theta= \pi/6$$ in Desmos since all function have to be functions of r but it is easy to see that it is a radial line.

Is the integral really from 6 to $$\pi/6$$? Are you sure it is not from 0 to $$\pi/6$$? That would make much more sense.

 

[karush]

$\textsf{a. Sketch the region of integration and evaluate.}\\$
\begin{align*}\displaystyle
\int_{0}^{\frac{\pi}{6}}
\int_{0}^{\sec{\theta}}
6r^{3} drd\theta\\
W|A=\frac{5}{3\sqrt{3}}
\end{align*}
OK I really didn't know how to do this in desmos

yes sorry it should be $\displaystyle\int_{0}^{\frac{\pi}{6}}$