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Definite integraton f(x) / sqrt (-x^2-bx-c)

  1. Jan 13, 2007 #1
    I am interested in the definite integration of
    f(x) / sqrt(-Q(x))
    over the range of x for which quadratic
    Q(x) = x^2 + b x + c is negative .

    f(x) = sin(a x)/x in particular but others too.

    Can anybody point me at any known formulae?

    TIA.
     
  2. jcsd
  3. Jan 13, 2007 #2
    This is a case for contour integration!
     
  4. Jan 13, 2007 #3
    Can you elaborate?

    Going complex, we might consider the imaginary part of
    exp ( i a z) / ( z sqrt(-(z-q1)(z-q2) )
    or more generally f(z) / sqrt(-(z-q1)(z-q2))
    as z moves along the real axis from q1 to q2 , the two real roots of quadratic Q(x)=x^2+bx+c.
     
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