Quite happy as a sum, why the ratio?
Calculus
Level
5
\[\displaystyle \int_{1}^{10} \dfrac{\{x\}}{\lfloor x \rfloor} \ dx\]
If the value of definite integral above can be written as \(\dfrac{a}{b}\) for coprime positive integers, find \(a+b\).
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 \(x\).
Also see product and sum of squares.
Read the brilliant.org wiki for further details.
by
Aditya Raut