# Easy As A Sum, But The Sum Of Squares?

Calculus Level 2

$\displaystyle \int_{0}^{12} \Bigl( \{x\}^2+\lfloor x \rfloor ^2\Bigr) \ dx = \ ?$

Details and assumptions:

• Every $$x\in \mathbb{R}$$ can be written as $$x=\lfloor x \rfloor + \{x\}$$.
• As usual, $$\lfloor x \rfloor$$ denotes greatest integer less than or equal to $$x$$.
• $$\{x\}$$ is the fractional part of $$x$$.
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