1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Integration of e

  1. Mar 5, 2012 #1
    1. The problem statement, all variables and given/known data
    I have the problem and answer, I'm just confused on the last step, but I'll put down everything anyways.

    Find the arclength of the curve r(t) = <5√(2)t, e5t, e-5t>

    2. Relevant equations

    L = ∫|r'(t)|

    3. The attempt at a solution

    r'(t) = √((5√(2))2+(5e5t)2+(-5e-5t)2)

    |r'(t)| = 5√(2+e10t+e-10t)

    Now this is where I get confused.

    ∫(5√(2+e10t+e-10t)) = ((e10t-1)*√(2+e10t+e-10t))/(e10t+1)

    I just don't understand how to integrate my answer to get that. If someone could just go through the steps that'd be great. Thanks!

    Then obviously sub in for 1 and 0, getting 148.4064 which is correct so I know that the integration is correctly done.
    Last edited: Mar 5, 2012
  2. jcsd
  3. Mar 5, 2012 #2


    User Avatar
    Science Advisor
    Homework Helper

    That's an odd form for the resulting integral. To see how to do it more easily what is (e^(5t)+e^(-5t))^2? Expand it out.
  4. Mar 5, 2012 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Your function [itex] 5\sqrt{2 + e^{10t} + e^{-10t}}[/itex] can be re-written, using the identity [itex] \cosh(10t) =2 \cosh(5t)^2 - 1,[/itex] to give a much simpler integral.

    Last edited: Mar 5, 2012
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook