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Let f : R to R is a function defined as ...

Let `f : R to R` is a function defined as `f(x)` where `= {(|x-[x]| ,:[x] "is odd"),(|x - [x + 1]| ,:[x] "is even"):}`
[.] denotes the greatest integer function, then `int_(-2)^(4) dx` is equal to

A

`int_(2)^(4)f(x)dx=1`

B

`int_(2)^(4)f(x)dx=3`

C

`int_(-10)^(10)f(x)dx=10`

D

`int_(-1)^(1)f(x)dx=0`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C

`x-[x]={x}`
`x-[x+1]={x}-1`
`int_(-2)^(4)f(x)dx=6,(1)/(2)(1.1)=3`
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