Question

For any real number x, let [ x ] denote the largest integer less than equal to x Let f be a real valued function defined on the interval [-10,10] by $f(x)=\begin{cases} x-[x], & \text { if }(x) \text { is odd } \\\ 1+[x]-x & \text { if }(x) \text { is even }\end{cases}$Then the value of$\frac{\pi^2}{10} \int\limits_{-10}^{10} f(x) \cos \pi x d x$ is :

• A. 4
• B. 2
• C. 1
• D. 0

Answer 1

Answer: (A)

4

Answer 2

The correct option is(A): 4.