Consider-a-continuously-differentiable-function-f-0-1-R-such-that-f-0-0-and-f-1-1-Find-the-minimum-value-of-0-1-f-x-2-1-x-2-dx-

Question Number 125621 by ZiYangLee last updated on 12/Dec/20

Consider a continuously differentiable

function f : [0, 1] \to R such that f (0) = 0

and f (1) = 1 . Find the minimum

value of \int_{0}^{1} {(f^{'} (x))}^{2} \sqrt{1 + x^{2}} d x