Chapter 5.6, Problem 58ES

Define $F\left(x\right)$ by

$F\left(x\right)={\displaystyle {\int }_{\pi /4}^x\cos 2tdt}$

(a) Use Part $2$ of the Fundamental Theorem of Calculus to find $F^{\prime }\left(x\right)$ .

(b) Check the result in part (a) by first integrating and then differentiating.