# Homework Help: Find the arc length of f(x) (x^(5/4))/5

1. May 16, 2010

### Bryon

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

find the arc length of f(x) (x^(5/4))/5.
The integration limits are from 0 to 4.

2. Relevant equations

The arc length formula is integrate sqrt(1 + (f'(x))^2)

3. The attempt at a solution

f'(x) = (5/4)*(1/5)*x^(1/4) = x^(1/4)/4

integral of sqrt(1 + (x^(1/4)/4)^2) = integral of sqrt(1 + sqrt(x)/16)

The part I am stuck on is getting rid of either sqrt roots.

Ive tried this: integral of sqrt(sqrt(x)/sqrt(x)/ + x/(sqrt(x)16))
but that didnt get me any where....Any idea how to simplify this? Im thinking that there is some sort of algebraic simplification that I am missing.

2. May 16, 2010

### gabbagabbahey

Why not start by trying the substitution [tex]u=1+\frac{\sqrt{x}}{16}[/itex]?

3. May 16, 2010

### LCKurtz

Try letting x = u2 followed by v = 1 + (1/16)u.

4. May 16, 2010

### julian92

just make the integral like this >>> int of (1/4)Sqrt(16+ Sqrt(x)) dx

then you can substitute >> u = 16 + sqrt(x)

it'll be easy ;)

Last edited: May 17, 2010
5. May 17, 2010

### Bryon

Wow...what a novice mistake I made! Thanks!