find-f-0-1-R-such-that-a-0-1-fdt-0-1-1-df-dt-2-dt-b-x-0-1-0-x-fdt-0-x-1-df-dt-2-dt-

Question Number 1472 by 123456 last updated on 11/Aug/15

find f : [0, 1] \to R such that

a . \underset{0}{\int^{1}} f d t = \underset{0}{\int^{1}} \sqrt{1 + {(\frac{d f}{d t})}^{2}} d t

b . \forall x \in [0, 1]

\underset{0}{\int^{x}} f d t = \underset{0}{\int^{x}} \sqrt{1 + {(\frac{d f}{d t})}^{2}} d t

Commented by prakash jain last updated on 13/Aug/15

f (t) = \cosh t

f (t) = 1