Easy As A Sum, So Why The Product?

Calculus Level 2

\[ \displaystyle \int_{0}^{20} \Bigl(\lfloor x \rfloor \{x\} \Bigr) \ dx = \ ? \]

Details and assumptions:

  • Every \(x\in \mathbb{R}\) can be written as \(x=\lfloor x \rfloor + \{x\} \).

  • \(\lfloor x \rfloor\) denotes greatest integer less than or equal to \(x\).

  • \(\{x\} \) is the fractional part of \(x\).

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