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Question

If [y] = the greatest integer less than or equal to y then 3π/2π/2[2sinx]dx is

A
π
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B
0
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C
π2
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D
π2
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Solution

The correct option is B π2
I=3π2π2[2sinx]dx ...(1)
Using property baf(x)dx=baf(a+bx)dx
I=3π2π2[2sin(3π2+π2x)]dx=3π2π2[2sin(x)]dx=3π2π2[2sin(x)]dx ...(2)
Adding (1) and (2) and using [x]+[x]=1
We get
2I=3π2π2(1)dx=[x]3π2π2=πI=π2

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