# Arc length and surfaces

1. Feb 9, 2009

### nameVoid

HELP
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Feb 9, 2009

### Staff: Mentor

What, are we supposed to guess what the problem is from the title on the thread? Presumably you want to find the arc length along the curve between points A and B.

What does this have to do with surfaces, though?

For the arc length, the integrand is sqrt(1 + (y')^2), which can be written as
$$\sqrt{1 + (\frac{x^2}{4} - \frac{1}{x^2})^2}$$
$$=\sqrt{1 + \frac{x^4}{16} -1/2 + \frac{1}{x^4}}$$

The last three terms under the radical are a perfect square. When you add the first term, you'll still have a perfect square, which makes it easy to take the square root, which means you'll have an easy function to integrate.