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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