allery$\int_0^{\pi/2} \cos^3 x\,dx$ equals:
A$1/3$
B$2/3$
C$3/4$
D$\pi/4$
Answer & Solution
Correct answer: B. $2/3$
Use $\cos^3 x = (1/4)(\cos 3x + 3\cos x)$.
**Integrating:** $(1/4)[\sin 3x/3 + 3\sin x]_0^{\pi/2} = (1/4)[(-1/3 + 3) - 0] = (1/4)(8/3) = 2/3$.
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