Find the length of the curve $\displaystyle r = \theta^2 $ from $\displaystyle \theta = 0 $ to $\displaystyle \theta=11$
The polar arc length formula is:
$\displaystyle \int_{\alpha}^{\beta}\sqrt{r^{2}+(\frac{dr}{d\thet a})^{2}}d{\theta}$
=$\displaystyle \int_{0}^{11}\sqrt{{\theta}^{4}+4{\theta}^{2}}$
=$\displaystyle \int_{0}^{11}[{\theta}\sqrt{{\theta}^{2}+4}]d{\theta}$
Can you finish?.