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Question

# Use the formula below to calculate the arc length of the polar curve.Formula:$L=\int_\alpha^\beta\sqrt{[f(\theta)]^2+[f'(\theta)]^2}d\theta=\int_\alpha^\beta\sqrt{r^2+\left(\frac{dr}{d\theta}\right)^2}d\theta$The entire cardioid r = a(1 − cos theta)

Solution

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The arc length is:

$L=\int\limits_\alpha^\beta\sqrt{r^2+\left (\dfrac{dr}{d\theta}\right )^2}d\theta$

where the parameter $\theta$ is defined on the interval $[\alpha,\beta]$.

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