Let `f:RtoR,f(x)={:(|x-[x]|,[x] "is odd"),(|x-[x+1]|,[x] "is even"):}` where [.] denotes greatest integer function, then

Options

A. `(5)/(2)`
B. `(3)/(2)`
C. 5
D. 3

Answer

D

Explanation

We have,
`f(x)={{:(|x-[x]|,"when[x]is odd"),(|x-[x]-1|,"when [x] is even"):} " " [ {:( :. ,[x+1]),(=,[x]+1)]`:}
`rArr f(x)={{:({x},"when[x]is odd"),(1-{x},"when [x] is even"):} `
The graph of f(x) is as shown in Fig. 12.

Clearly, `underset(-2)overset(4)int f(x)dx=6underset(-2)overset(-1)int f(x)dx=6xx(1)/(2)=3`