Chapter 11.12, Problem 5P

In Problems 4 to 13, identify each of the integrals as an elliptic integral (see Examples 1 and 2 ). Learn the notation of your computer program (see Problem 3 ) and then evaluate the integral by computer.

${\displaystyle {\int }_0^{\pi /2}\sqrt{1-\frac{1}{9}{\sin }^2\theta }}d\theta$