# 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 $$f\left( x \right)$$.

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