Change to …, …, …, and repeat … on

Change to $x=\sin \theta$, $\sqrt{1-x^2}=\cos \theta$, $dx=\cos \theta d\theta$, and repeat $T_4$ on ${\int }_0^{\pi /2}{\cos }^2\theta d\theta$. What is the predicted error after the change to $\theta$?

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §5.8 Numerical Integration, #18