Find the exact length of the polar curve described by: r=6 e^{-\theta} on the interval ...

Question:

Find the exact length of the polar curve described by: {eq}r=6 e^{-\theta} {/eq} on the interval {eq}\frac{5}{2} \pi \leq \theta \leq 6 \pi {/eq}

Length:

To find the arc length we will use the formula {eq}=\int \sqrt{r^{2}+\left ( \frac{\mathrm{d} r}{\mathrm{d} \theta} \right )^{2}}d\theta\\ {/eq} wheer we will put the value of r and differentiate it.

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To find the arc length we will use the formula

{eq}=\int \sqrt{r^{2}+\left ( \frac{\mathrm{d} r}{\mathrm{d} \theta} \right...

Arc Length of a Sector: Definition and Area

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Chapter 9 / Lesson 10
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Learn how to find the arc length of a sector with the formula and examples. Understand the formula and the method to find the area of a sector with examples.