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Math Help - Completing this integration

  1. #1
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    Completing this integration

    First I started out with

    <br />
\int \sqrt{x^2 - 4} dx<br />

    and I used  x = 2sec\theta

    where I am now is
    <br />
4\int \frac{sin^2\theta}{cos^3\theta} d\theta<br />

    how do I complete this?
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  2. #2
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    Quote Originally Posted by larryboi7 View Post
    First I started out with

    <br />
\int \sqrt{x^2 - 4} dx<br />

    and I used  x = 2sec\theta

    where I am now is
    <br />
4\int \frac{sin^2\theta}{cos^3\theta} d\theta<br />

    how do I complete this?
    You have 4\int \frac{\sin^2\theta}{(1 - \sin^2 \theta) \cos \theta} \, d\theta. Now make the substitution u = \sin \theta.
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  3. #3
    MHF Contributor Calculus26's Avatar
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    See attachment

    no point in converting to sines and cosines as sin^2(t) =1-cos^2(t)

    and you end up with sec^3(t) -sec(t) anyway
    Attached Thumbnails Attached Thumbnails Completing this integration-integral.jpg  
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