# Arc Length of e^5x from 0 to ln(4)

1. Feb 22, 2010

### Oblakastouf

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

http://i47.tinypic.com/1z6naa.jpg

Note... I used wolfram alpha to get the answer, I did not get it myself... So I still need help. The answer shown is correct, so you'll know if you got it.

2. Relevant equations

Integral [0, ln(4)] sqrt(1+(dy/dx)^2)

3. The attempt at a solution

2pi Integral [0, ln(4)] y*sqrt(1+(dy/dx)^2)

2pi Integral [0, ln(4)] (e^5x)*sqrt(1+5e^5x^2)dx

u = 5e^5x
du = 25e^5x dx
dx = du/25e^5x

2pi Integral [0, ln(4)] (e^5x)*sqrt(1+u^2)du/25e^5x

2pi Integral [0, ln(4)] sqrt(1+u^2)du

u = tan(t)

2pi/25 Integral [0, ln(4)] sqrt(1+tan^2(t))du

2pi/25 Integral [0, ln(4)] sqrt(sec^2(t))du

2pi/25 Integral [0, ln(4)] sec(t)du

du = sec^2(t)dt
dt = du*cos^2(t)

2pi/25 Integral [0, ln(4)] cos^2(t)/cos(t)dt

2pi/25 Integral [0, ln(4)] cos(t)dt

Edit bounds...

[arctan(5), arctan(5e^(5*ln(4)))]

Then get ****ed over with an answer of .0048...

What did I do wrong.

Last edited: Feb 22, 2010
2. Feb 22, 2010

### Roni1985

the question asks the surface area and not the arc length. Perhaps this is your mistake

3. Feb 23, 2010

### mmmboh

I have never heard of wolfram alpha before...very interesting. What did you type in to get the answer to your question? I can't figure it out...