Find the area out of the functional
Calculus
Level
3
If \(f\) is a real-valued function such that \( f(x) \neq 0 \) for all real \(x\), and satisfies the functional equation \[\large f(x)=x\sqrt{x\sqrt{x\sqrt{x \sqrt{f(x)}}}}\] for all \(x>0\). Then find the area under the graph of \(f\) between \(x=1\) to \(x=4\).
Note: This is my original problem. For more of my problems check the set Questions I've Made
by
Sanjeet Raria