The value of int(-g)^1 [x[1+cos((pix)/2)...

The value of `int_(-g)^1 [x[1+cos((pix)/2)]+1] dx,` where [.] denotes greatest integer function is

A

`1`

B

`1//2`

C

`2`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:

C

From graph `int_(-2)^(1)[x[1+"cos"(pix)/2]+1]dx`
`=int_(-2)^(-1) [x[1+(-1)]+1]dx+int_(-1)^(1)[x[10]+1]dx`
`=(x)_(-2)^(-1)+int_(-1)^(1)[x+1]dx`
`=(-1-(-2))+int_(-1)^(0)0dx+int_(0)^(1)1dx=2`

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