- #1

karush

Gold Member

MHB

- 3,269

- 5

$\tiny{up 244.14.4.26}$

$\textit{a. Sketch the region of Intregration}$

$\textit{b. convert the sum of integrals to a Cartesian sum of Integrals:}$

\begin{align*}\displaystyle

I_{26}&=\int_{0}^{\tan^{-1}(4/3)}

\int_{0}^{3\sec{\theta}}

r^7 \, dr \, d\theta

+\int_{\tan^{-1}(4/3)}^{\pi/2}

\int_{0}^{4\csc\theta}

r^7 \, dr \, d\theta\\

&=\int_{0}^{\tan^{-1}(4/3)}\Biggr|\frac{r^8}{8}\Biggr|_0^{3\sec{\theta}} \, d\theta

+\int_{\tan^{-1}(4/3)}^{\pi/2}\Biggr|\frac{r^8}{8}\Biggr|_{0}^{4\csc\theta} \, d\theta

\end{align*}

next ?

OK first I don't how you plot $r^7$ on Desmos

$\textit{a. Sketch the region of Intregration}$

$\textit{b. convert the sum of integrals to a Cartesian sum of Integrals:}$

\begin{align*}\displaystyle

I_{26}&=\int_{0}^{\tan^{-1}(4/3)}

\int_{0}^{3\sec{\theta}}

r^7 \, dr \, d\theta

+\int_{\tan^{-1}(4/3)}^{\pi/2}

\int_{0}^{4\csc\theta}

r^7 \, dr \, d\theta\\

&=\int_{0}^{\tan^{-1}(4/3)}\Biggr|\frac{r^8}{8}\Biggr|_0^{3\sec{\theta}} \, d\theta

+\int_{\tan^{-1}(4/3)}^{\pi/2}\Biggr|\frac{r^8}{8}\Biggr|_{0}^{4\csc\theta} \, d\theta

\end{align*}

next ?

OK first I don't how you plot $r^7$ on Desmos

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