Mathematics

Mathematics

Problem

For any real number xx, let [x][x] denote the largest integer less than or equal to xx. Let ff be a real valued function defined on the interval [−10,10][-10, 10] by f(x)={x−[x]if [x] is odd1+[x]−xif [x] is evenf(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 π210∫−1010f(x)cos⁡πx dx\frac{\pi^2}{10} \int_{-10}^{10} f(x) \cos \pi x \, dx is [JEE 2010]

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