Question

What is the value of \[\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\sin^{2}x\,dx\]?

Options

• \[\frac{\pi}{6}\]

• \[\frac{\pi}{12}\]

• \[\frac{\pi}{4}-\frac{1}{2}\]

• \[\frac{\pi}{4}+\frac{1}{2}\]

Answer 1

Use \[\sin^{2}x=\frac{1-\cos 2x}{2}\] after applying the even-function property. The resulting value is \[\frac{\pi}{4}-\frac{1}{2}\].