1. Find the length of the curve $r = \cos^3\frac{\theta}{3}$, $0 \le \theta \le \pi/4$.
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The arc length formula for a curve given in polar coordinates is: \[L = \int_{\theta_1}^{\theta_2} \sqrt{r^2 + \left(\frac{dr}{d\theta}\right)^2} d\theta\] where \(r\) is the function that defines the curve and \(\frac{dr}{d\theta}\) is the derivative of \(r\) Show more…
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