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: Option C
Explanation
(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})