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Math Help - Hard Trig Sub Need Help asap

  1. #1
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    Hard Trig Sub Need Help asap

    Integral of 1/[(x^5)(9x^2-1)^(.5)] dx from sqrt(2)/3 to 2/3.
    everyway i try it, it seems to be wrong!! i have been doing this problem for hours! i need help

    here is my work: http://i198.photobucket.com/albums/a...n/scan0002.jpg
    http://i198.photobucket.com/albums/a...scan0003-1.jpg

    also I am not sure if #15 on the second link is correct either.
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  2. #2
    Super Member Random Variable's Avatar
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    You forgot to change the limits of integration after you made the substitution.

     81 \int_{ \pi /4}^{\pi /3} \cos^{4} \theta \ d \theta
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  3. #3
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    ?

    wait how did you do that?
    it got me the right answer, but how did you change the limits?
    Last edited by Jasonium; June 23rd 2009 at 09:40 PM.
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  4. #4
    Super Member Random Variable's Avatar
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    Quote Originally Posted by Jasonium View Post
    wait how did you do that?
     \frac {\sqrt{2}}{3} = \frac {1}{3} \sec \theta

     \sqrt{2} = \sec \theta

    \frac {1}{\sqrt{2}} = \cos \theta

     \theta = \frac {\pi}{4}


     \frac {2}{3} = \frac {1}{3} \sec \theta

     \frac {1}{2} = \cos \theta

     \theta = \frac {\pi}{3}
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  5. #5
    Senior Member apcalculus's Avatar
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    Quote Originally Posted by Jasonium View Post
    Integral of 1/[(x^5)(9x^2-1)^(.5)] dx from sqrt(2)/3 to 2/3.
    everyway i try it, it seems to be wrong!! i have been doing this problem for hours! i need help

    here is my work: http://i198.photobucket.com/albums/a...n/scan0002.jpg
    http://i198.photobucket.com/albums/a...scan0003-1.jpg

    also I am not sure if #15 on the second link is correct either.
    First substitute u = 3x with dx = (1/3) du

    so the integrand becomes
    <br />
\frac{3^5}{u^5\sqrt{u^2-1}} \frac{1}{3} du

    Then substitute:

    u = \sec \theta

    note that:
    du = \sec \theta \tan \theta

    and the integrand becomes:
    <br />
\frac{3^4}{(\sec \theta)^5 \tan \theta} \sec \theta \tan \theta

    which reduces to

    \frac{81}{(\sec \theta)^4}<br />
    OR
    <br />
81 (\cos \theta)^4

    The integral of the fourth power of the cosine function is:

    (12 x + 8 Sin[2 x] + Sin[4 x])
    ----------------------------
    32

    I hope this helps.
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