don't understand the value of a sum in a curve that has arc length

Hi there

I've got a curve in $\displaystyle \mathbb{R}^3: \gamma(x):=(f(u),0,h(u))$ I know that f(x) is always bigger than zero and the parameter x is between 0 and 1.

Now $\displaystyle \gamma$ has arc length which means

$\displaystyle \int_0^1 |\gamma'| dx=\int_0^1 \sqrt{ f'(x)^2+h'(x)^2 } dx = 1$. Well somenone today told me that then

$\displaystyle \sqrt{f'(x)^2+h'(x)^2}=1$ must be true. Can someone please explain me why this is true or isn't it true? Yet I don't understand why this has to be equal to 1...

Regards

Re: don't understand the value of a sum in a curve that has arc length

a curve is said to be parameterized by arc length if its tangent vector is of unit length.