# A simple double integral.

Calculus Level 5

Let : $I= \int_0^1 \int_0^1 \left\{ \frac{x}{y} \right\} \ \mathrm{d}x\ \mathrm{d}y$ Find $$\lfloor1000I\rfloor$$.

$$\{x\}$$ denotes to the fractional part of $$x$$, and $$\lfloor x\rfloor$$ denotes to the floor function for $$x$$.

Remark : Numerical integration using software can be wrong.

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