# Inspired by Michael Mendrin

**Calculus**Level 5

A rectangle's base lie on the \(x\)-axis while it's top corners are on the curve \(\displaystyle y =\dfrac{x}{x^2 + 1}\). Now a cylinder is obtained by revolving Rectangle about x-axis, if the maximum volume of cylinder is \(V_{max}\). Find \(\displaystyle \lfloor 1000V_{max} \rfloor \).

Inspired by this awesome problem