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 Evaluate 02π[sinx]dx, where [.] denotes  the greatest integer function. 

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a
b
π
c
d
-2π

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detailed solution

Correct option is A

y=sin⁡x is a non-monotonic function in [0,2π] .  Hence, draw the graph of f(x)=[sin⁡x] .  From the above graph we have, ∫02π [sin⁡x]dx= Algebraic area of the shaded region  =(π)(−1) (l×b) =−π

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