Let f(x)=max. {x+|x|,x-[x]} , where [x] ...

Let `f(x)=max. {x+|x|,x-[x]}` , where [x] denotes the greatest integer less than or equal to x, then `int_(-2)^(2) f(x)` is equal to

A

3

B

5

C

1

D

none of these

Text Solution

Verified by Experts

The correct Answer is:

B

Since `x+|x|gtx-[x]"for all" x gt0` and `x+|x|=0 le x -[x] "for all" x lt0`
`:.underset(-2)overset(2)int f(x)dx=underset(-2)overset(0)int (x-[x])dx+underset(0)overset(2)int (x+x|)dx`
`rArrunderset(-2)overset(2)int f(x)dx=2xx(1)/(2)+underset(0)overset(2)int 2xx =1+4=5`

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