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Help with Trig Substitution Integral Problem

  1. Feb 25, 2014 #1
    1. The problem statement, all variables and given/known data

    Question is attached in this post.


    2. Relevant equations

    Question is attached in this post.

    3. The attempt at a solution

    I've solved the problem via using x=asinθ where a=1

    I've been able to integrate the problem to the point where I get cos^2(θ)/sin^2(θ), but can't seem to find a way to simply the problem further so that I can finish off the integration.

    The answer to the question is √3 - π/3
     

    Attached Files:

    Last edited: Feb 25, 2014
  2. jcsd
  3. Feb 25, 2014 #2

    Curious3141

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    Homework Helper

    Please show your steps in detail.
     
  4. Feb 25, 2014 #3
    I do not see how x=atanθ would help you in this problem .Instead try x=sinθ or cosθ.
     
  5. Feb 25, 2014 #4
    That was a typo, I actually did use asinθ.
     
  6. Feb 25, 2014 #5
    ∫√(1-sin^2(θ))/(sin^2(θ) dθ = ∫cos^2(θ)/sin^2(θ) dθ

    (I don't know how to simply the problem further, I know cos^2/sin^2=cot^2, but trying to get the integral of cot^2 isn't practical etc.)
     
  7. Feb 25, 2014 #6
    Okay...Now rewrite cot2θ in terms of cosec2θ .
     
  8. Feb 25, 2014 #7
    Thanks lol, I completely forgot about that identity since I haven't used that specific one in a long time etc.
     
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