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Thread: calculate

  1. #1
    Super Member dhiab's Avatar
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    calculate

    CALCULATE THIS INTEGRAL : <br />
\int\limits_0^{\frac{\pi }{2}} {\left( {\frac{{\sqrt {\sin x} }}{{\sqrt {\sin x} + \sqrt {\cos x} }}} \right)} dx
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  2. #2
    MHF Contributor
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    Talking

    Wolfram's The Integrator returns the following:

    Code:
    (x + Log[Cos[x] - Sin[x]] + 
     
        (4 Sqrt[Cos[x]] ((1 - I) 
     
                                              x
              EllipticPi[-I, -ArcSin[Sqrt[Tan[-]]], -1] + 
                                              2
     
                                                    x
             (1 + I) EllipticPi[I, -ArcSin[Sqrt[Tan[-]]], 
                                                    2
     
                                     1
               -1] - EllipticPi[------------, 
                                -1 + Sqrt[2]
     
                               x
              -ArcSin[Sqrt[Tan[-]]], -1] - 
                               2
     
                               1
             EllipticPi[-(-----------), 
                          1 + Sqrt[2]
     
                               x                   x
              -ArcSin[Sqrt[Tan[-]]], -1]) Sqrt[Tan[-]]) / 
                               2                   2
     
                          x 2
         (Sqrt[Cos[x] Sec[-] ] Sqrt[Sin[x]])) / 2
                          2
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  3. #3
    Math Engineering Student
    Krizalid's Avatar
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    no, no, these integrals are made to solve them without computing the antiderivative since in many cases you won't be able to find it.

    work a general problem and compute \int_0^{\frac\pi2}\frac{f(\sin x)}{f(\sin x)+f(\cos x)}\,dx.
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