Let $f: R \rightarrow R, f(x)=\left\{\begin{array}{c}|x-[x]|,&[x] \text { is odd } \\ |x-[x+1]|,&[x] \text { is even }\end{array}\right.$, where [.] denotes greatest integer function, then $\int\limits_{-2}^4 f(x) dx$ is equal to
Answer & explanation
Correct answer: option 4
$x-[x]=\{x\}$
$x-[x+1]=\{x\}-1$
$\int\limits_{-2}^4 f(x) d x=6 . \frac{1}{2}(1.1)=3$
Hence (4) is the correct answer.