Question
Find the lengths of the curves.$$\text { The curve } r=\sqrt{1+\sin 2 \theta}, \quad 0 \leq \theta \leq \pi \sqrt{2}$$
Step 1
Step 1: The length of a curve in polar coordinates is given by the formula: \[L = \int_{a}^{b} \sqrt{r^2 + \left(\frac{dr}{d\theta}\right)^2} d\theta\] where \(r\) is the polar function, \(\frac{dr}{d\theta}\) is its derivative with respect to \(\theta\), and the Show more…
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