Question

The value of $\frac{6}{\pi }\underset{\pi /6}{\overset{\pi /3}{\int }}[2\sin x]dx$, where [.] represents greatest integer function is

• A. 1
• B. 2
• C. 3
• D. 0

Answer 1

Answer: (A)

$\frac{\pi }{6}<x<\frac{\pi }{3}\Rightarrow \frac{1}{2}<\sin x<\frac{\sqrt{3}}{2}$
$\Rightarrow 1<2\sin x<\sqrt{3}$
$\therefore [2\sin x]=1$