Evaluate the integral \(\int^{\frac{\pi}{4}}_{\frac{\pi}{12}} 2 \cos 2x \mathrm {d} x\)

A.

-\(\frac{1}{2}\)

B.

-1

C.

\(\frac{1}{2}\)

D.

1

Correct answer is C

\(\int_{\frac{\pi}{12}} ^{\frac{\pi}{4}} 2 \cos 2x \mathrm {d} x\)

= \([\frac{2 \sin 2x}{2}]|_{\frac{\pi}{12}} ^{\frac{\pi}{4}}\)

= \(\sin 2x |_{\frac{\pi}{12}} ^{\frac{\pi}{4}}\)

= \(\sin 2(\frac{\pi}{4}) - \sin 2(\frac{\pi}{12})\)

= \(\sin \frac{\pi}{2} - \sin \frac{\pi}{6}\)

= \(1 - \frac{1}{2} = \frac{1}{2}\)