# Finding the length of a graph

1. Sep 21, 2008

### cse63146

1. The problem statement, all variables and given/known data
Determine the length of the following graph:

$$f(x) \ = \ \frac{x^5}{10} + \frac{1}{6x^3}$$

2. Relevant equations

length of a graph: $$\int \sqrt{1 + f'(x)^2}dx$$

3. The attempt at a solution

so $$f'(x) = \frac{x^4}{2} -\frac{1}{18x^4}$$

$$f'(x)^2 = \frac{x^8}{4} + \frac{1}{18} + \frac{1}{324x^8}$$

Is f'(x)^2 correct?

Did I even need to expand, or is there some trick to this?

2. Sep 21, 2008

### Dick

There is almost always a trick to length of arc problems and the trick is almost always make the expression under the radical into a perfect square. Add 1 to f'^2 and you will see that you can. Except fix f'(x) first. I get x^4/2-1/(2*x^4). Why don't you?

Last edited: Sep 21, 2008
3. Sep 21, 2008

### cse63146

I see what I did wrong. I "brought up" the 6 as well, so I wrote it as 6x^-3

4. Sep 21, 2008

### Dick

Ok, so can you square it and then express the expression under the radical as a perfect square? I'm betting you can.