# Do you know this property?

**Calculus**Level 5

\(f(x)\) is a monotonically strictly increasing function in \([3,5]\) such that \[ \int _{ 3 }^{ 5 }{ { \left( f (x) \right) }^{ 2 }dx=9 } \quad \quad f\left( 3 \right) =1 \quad \quad f\left( 5 \right) =4\]

Find the value of \[2\int _{ 1 }^{ 4 } x\left( 5-f^{ -1 }(x) \right) dx\]

**Notation:** \(f^{ -1 }\left( x \right) \) denotes the inverse of \(f\left( x \right)\).