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Math Help - difficult integral

  1. #1
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    difficult integral

    could you help me please to solve this integral

    sqrt(1+4sin^(2)(x))

    from x=0 to x= pi/2
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  2. #2
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    Quote Originally Posted by ameer View Post
    could you help me please to solve this integral

    sqrt(1+4sin^(2)(x))

    from x=0 to x= pi/2
    This integral is not expressible in terms of elementary functions.
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  3. #3
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    This is an Elliptic Integral:

    \int_{0}^{\frac{\pi}{2}}\sqrt{1+4sin^{2}(x)}dx=\sq  rt{5}\text{Elliptic}\left(\frac{2}{\sqrt{5}}\right  )
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  4. #4
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    Thank you!
    I really appreciate your help.
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