Greatest Integer+Trigonometric Integrals

Calculus Level 4

\(\displaystyle\int_{0}^{n} cos(2\pi\lfloor x \rfloor {x})\)=?

Note:

  1. \(\lfloor x \rfloor\) denotes greatest integer less than or equal to x.
  2. {x} denotes fractional part of x.
  3. \(\lfloor x \rfloor + {x}=x\)

Note:This question is a part of set KVPY 2014 SB

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