Arc length help

[intervade]

Hello,

I'm given this problem: the graph of y = f(x) passes through the origin. The arc length from (0,0) to (x, f(x)) is s(x) integral[ (1+e^2)^(1/2) ]dt from 0 to x. Determine the function f(x)... now can I assume based on arc length I know that f'(x)^2 = e^t ? Aside from that, I'm not really where to being.

 

[tutor_joel]

did you write that correctly? should it be e^2 or e^x, or e^t in the integral? Otherwise you're integrating a constant.
And is it S(x) = intergral, or s(x)*integral?

 

[intervade]

oops! I cant type. It is e^t and s(x) IS the integral

 

[JuicyBurger]

now can I assume based on arc length I know that f'(x)^2 = e^t

So.... if

\(\displaystyle f'(x)^2 = e^t\)

then

\(\displaystyle f'(x) = \sqrt{e^t} = e^{\frac{1}{2}t}\)

\(\displaystyle f(x) = \int_{}{}f'(x) = \int_{}{} e^{\frac{1}{2}t}\)

Correct?

Hope this helps!

(edits were because I hit the submit too early!)