Help with arc lenght properties

[mapacheloco182]

Hey guys, i need some help with this excersice below.
Find the equation of the curve that passes through (0,1) using the following property:
-The area under the curve limited by the coordinate axes and the ordinate of any point is equal to the length of the curve corresponding to that region.

 

[Steven G]

Hi, I am sorry but this is not a forum where we solve problems for student. On this forum we prefer to help students solve their own problems with our helpful hints.
We would love to help you but 1st you need to tell us where you are stuck and post the work you have done so far.

 

[Romsek]

sounds like you need to solve the integral equation

[MATH]\displaystyle \int \limits_a^b ~f(t)~dt = \int \limits_a^b \sqrt{1+f^\prime(t)}~dt,~\forall a < b \leq 1[/MATH]