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Arc length of polar curves - Parametric Equations and Polar Coordinates

Arc length of polar curves

In this lesson, we will learn how to find the arc length of polar curves with a given region. We will first examine the formula and see how the formula works graphically. Then we will apply the formula to some of the questions below. Make sure you know trigonometric identities very well, as you will often need to use substitution to make your integrals simpler to integrate.

Lessons

Notes:
Let r=f(θ)r=f(\theta) be a polar curve and αθβ\alpha \leq \theta \leq \beta.
Then we use the following formula to calculate the arc length of the curve:
L=αβr2+(drdθ)2dθL=\int_{\alpha}^{\beta}\sqrt{r^2+(\frac{dr}{d\theta})^2}d\theta
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Arc length of polar curves

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