A simple double integral.

Calculus Level 5

Let : I=0101{xy} dx dyI= \int_0^1 \int_0^1 \left\{ \frac{x}{y} \right\} \ \mathrm{d}x\ \mathrm{d}y Find 1000I\lfloor1000I\rfloor.


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

Remark : Numerical integration using software can be wrong.

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