1. Not finding help here? Sign up for a free 30min 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!

Trigonometric Substitution problem

  1. Sep 14, 2013 #1
    1. [itex]∫\frac{\sqrt{x^{2}-4}}{x} dx[/itex], [itex]x=2secθ[/itex], [itex]dx=2secθtanθ dθ[/itex]



    2. [itex]\sqrt{x^{2}-a^{2}}[/itex],[itex]sec^{2}θ-1=tan^{2}θ[/itex]



    3. [itex]\sqrt{x^{2}-4}=\sqrt{4sec^{2}θ-4}=\sqrt{4(1+tan^{2}θ)-4}=\sqrt{4tan^{2}θ}=2\left|tanθ\right|=2tanθ[/itex];[itex]∫\frac{\sqrt{x^{2}-4}}{x}dx=∫\frac{2tanθ}{2secθ}dθ=\frac{ln\left|secθ\right|}{ln\left|secθ+tanθ\right|}+C=ln\left|secθ\right|-ln\left|secθ+tanθ\right|+C[/itex];[itex]∫\frac{\sqrt{x^{2}-4}}{x}dx=ln\left|\frac{x}{2}\right|-ln\left|\frac{x}{2}+\frac{\sqrt{x^{2}-4}}{2}\right|+C=ln\left|x\right|-ln\left|2\right|-ln\left|x+\sqrt{x^{2}-4}\right|+ln\left|2\right|+C[/itex]. Please tell me what I did wrong.
     
  2. jcsd
  3. Sep 14, 2013 #2

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    What happened to the substitution for dx in terms of dθ?
     
  4. Sep 14, 2013 #3
    I see what you mean. Ok, here is what I have after the dx substitution: [itex]\int\frac{\sqrt{x^{2}-4}}{x}dx = \int\frac{2tanθ}{2secθ}2secθtanθdθ = 2\int tan^{2}θdθ[/itex]
     
  5. Sep 14, 2013 #4
    Which is: [itex]2\int(sec^{2}θ-1)dθ = 2(tanθ-θ)+C[/itex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Trigonometric Substitution problem
Loading...