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: Surface Area of y = e^5x revolved around the x-axis from 0 to ln(4)

  1. Feb 23, 2010 #1
    1. The problem statement, all variables and given/known data


    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.
  2. jcsd
  3. Feb 23, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper

    If du=sec^2(t)*dt, then sec(t)*du is sec^3(t)*dt.
  4. Feb 23, 2010 #3
    Right... My mistake, but I'm also having trouble with integration, and that isn't my strong suit, how would I integrate that?
  5. Feb 23, 2010 #4


    User Avatar
    Science Advisor
    Homework Helper

    It's kind of a long haul. You start by integrating by parts u=sec(t), dv=sec(t)^2*dt. It probably goes a little easier if you go back to the integral of sqrt(1+x^2)*dx and substitute x=sinh(u), if you are ok with hyperbolic functions.
  6. Feb 23, 2010 #5
    I am, but I'm in a class that doesn't use them yet lol.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook