# Fractional parts in frenzy

Calculus Level 3

$\frac {\displaystyle \int _{ 0 }^{ 12 }{ x\left\lfloor x \right\rfloor dx } }{\displaystyle \int _{ 0 }^{ 12 }{ \left\{ x \right\} x\left\lfloor x \right\rfloor dx } } =\frac { A }{ B }$

If the above is true, where $$A$$ and $$B$$ are coprime positive integers, find $$\displaystyle A+B$$

Notation:

• $$\left\{ x \right\}$$ is the fractional part function.
• $$\left\lfloor x \right\rfloor$$ is the floor function.
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