question_answer

Let \[f:R\to R\] be given by \[f(x)=\left\{ \begin{matrix}    |x-[x]|,\,\text{When}\,[x]\,\text{is}\,\text{odd}  \\    |x-[x]-1|,\,\text{When}\,[x]\,\text{is}\,\text{even}  \\ \end{matrix} \right.\] Where [.] denotes the greatest integer function, then \[\int\limits_{-4}^{4}{f(x)dx}\] is equal to

A)  5/2                                       

B)  3/2

C)  8                                            

D)  4

Correct Answer: D

Solution :

\[\because \,\,f(x)=\left\{ \begin{matrix}    \{x\}, & [x]\,\text{is}\,\text{odd}  \\    1-\{x\}, & [x]\,\text{is}\,\text{even}  \\ \end{matrix} \right.\] \[\therefore \] The graph of \[f(x)\] is \[\therefore \,\,\int\limits_{-4}^{4}{f(x)dx=8\int\limits_{0}^{1}{f(x)dx=4}}\]