The figure shows a pendulum with length $L$ that makes a maximum angle $\theta_0$ with the vertical. Using Newton's Second Law it can be shown that the period $T$ (the time for one complete swing) is given by $$T=4\sqrt{\frac{L}{g}}\int_{0}^{\,\pi/2} {\frac{1}{\sqrt{1-k^2\sin^2(x)}}}\,dx$$ where $k=\sin\left(\frac{1}{2}\theta_0\right)$ and $g$ is the acceleration due to gravity.

If $L$ = 1 m and $\theta_0=42^{\circ},$ use Simpson's Rule with $n$ = 10 to estimate the period. Give your answer correct to two decimal places.

Period $\approx$