Originally Posted by

**ecMathGeek** Thank you for the clarification. Everything you did is correct. I just wanted to be sure I understood the question you were asking.

I have a suggestion. Don't integrate this function horizontally. Try this instead:

INT[-y(x0) to +y(x0)] Sqrt(1 + (x')^2)dx

To do this, we need the vertical limits of this function.

Since it's a horizontal parabola, we will be integrating from y = -sqrt(2px0) to y = +sqrt(2px0)

Now, to find x'

x = y^2/(2p) --> x' = 2y/(2p) = y/p

Now, integrate:

INT[-sqrt(2px0) to sqrt(2px0)] Sqrt(1 + (y/p)^2) dy

Integrating this will involve a double substitution, but it is possible. Do you know how to use trig substitution?