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Math Help - Integration of roots...

  1. #1
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    Integration of roots...

    Hi all.

    My battle with calculus is forever ongoing, although I feel I've made lots of progress recently. However I am a bit unsure on how to go about the following:

    \int \sqrt{9 + cos x}

    I am aware that:

    \int \sqrt{9 + cos x}= \int (9 + cos x)^\frac{1}{2}

    but am still stumped.

    Any pointers would be greatly appreciated.

    Mav
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    First, you forgot dx....

    Second, I don't think that there is analytic function for your integral...
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  3. #3
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  4. #4
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    In other words, don't be upset that you could not integrate it. If it were \int \sqrt{1+ 9 cos^2(\theta)}d\theta then you could use the substitution [itex]u= 3 cos(\theta)[/itex] but as the integral is it cannot be integrated in terms of elementary functions- you must use the "elliptic integral of the second kind" which, itself, must be evaluated numerically.
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  5. #5
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    O.K.

    Would the same be true of:

    \int \sqrt{9 - sin x} dx

    I have the above as a denominator of a function and am using a separation of variables to find an implict solution.

    So I have \int \sqrt{9 - sin x} dx on one side of the equation because I multiplied through by it. So if I can't integrate it, what do I do?

    Confused.
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