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 problem

  1. Mar 28, 2010 #1
    The problem statement, all variables and given/known data
    Use appropriate substitution and than a trigonometric substitution and evaluate the integral.

    [tex]\int_{1}^{e}\frac{dy}{y\sqrt{1 + (lny)^{2}}}[/tex]

    The attempt at a solution

    [tex]\int_{1}^{e}\frac{dy}{y\sqrt{1 + (lny)^{2}}}[/tex]

    [tex]ln y = tan\theta[/tex]
    [tex]y = cos^{2}\theta[/tex]
    [tex]dy = -2cos\theta sin\theta d\theta[/tex]

    [tex]= -2\int_{1}^{e}\frac{cos\theta sin\theta d\theta}{cos^{2}\theta\sqrt{1 + tan^{2}\theta}}[/tex]

    [tex]= -2\int_{1}^{e}\frac{sin\theta d\theta}{cos\theta sec\theta}[/tex]

    [tex]= -2\int_{1}^{e}sin\theta d\theta[/tex]

    How do I proceed from here? I think I have to change the limits of integration in terms of [tex]\theta[/tex] instead of [tex]y[/tex].
    Last edited: Mar 28, 2010
  2. jcsd
  3. Mar 28, 2010 #2


    User Avatar
    Homework Helper

    From lny=tanθ, you should get that dy/y =sec2θ dθ

    giving you

    [tex]\int \frac{sec^2\theta}{\sqrt{1+tan^2 \theta}}d\theta[/tex]
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Similar Threads for Integration problem Date
Integration Problem Apr 3, 2018
Integration problem using u substitution Mar 19, 2018
Integration problem of a quotient Feb 20, 2018
Problem integral Nov 26, 2017
Integration by parts problem Jul 18, 2017