# 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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