Chapter 4.5, Problem 78E

Using Symmetry Use the symmetry of the graphs of the sine and cosine functions as an aid in evaluating each definite integral.

(a). ${\displaystyle {\int }_{-\pi /4}^{\pi /4}\sin xdx}$ (b). ${\displaystyle {\int }_{-\pi /4}^{\pi /4}\cos xdx}$

(c). ${\displaystyle {\int }_{-\pi /2}^{\pi /2}\cos xdx}$ (d). ${\displaystyle {\int }_{-\pi /2}^{\pi /2}\sin x\cos xdx}$