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Math Help - Integral of sqrt(1 + (cosx) ^ 2) ?

  1. #1
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    Integral of sqrt(1 + (cosx) ^ 2) ?

    Hi please help to solve this integral .

    <br />
\int\sqrt{1+cos^2x}dx<br />
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  2. #2
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    Quote Originally Posted by parkhid View Post
    Hi please help to solve this integral .

    <br />
\int\sqrt{1+cos^2x}dx<br />
    integrate Sqrt&#x5b;1 &#x2b; &#x28;Cos&#x5b;x&#x5d;&#x29;&#x5e;2&#x5d; - Wolfram|Alpha

    Where has the integral come from?
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  3. #3
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    The main question intend is to calculate the length of arc which

    will create by F(x) = Sin(X) from 0 to pi .

    so, we should calculate this : \int\sqrt{1+y'^2}dx

    and if we put cosx instead of y' we have the above integral.

    \int\sqrt{1+cos^2x}dx

    Iam very Now . what is ellipitic integral ??????
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  4. #4
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    Quote Originally Posted by parkhid View Post
    The main question intend is to calculate the length of arc which

    will create by F(x) = Sin(X) from 0 to pi .

    so, we should caclculate this : \int\sqrt{1+y'^2}dx

    and if we put cosx instead of y' we have the above integral.

    \int\sqrt{1+cos^2x}dx
    Well, as you can see, it can't be done using a finite number of elementary functions.
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  5. #5
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    Is There any other way to solve ?
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  6. #6
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    it's been asnwered before.
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