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How to integrate this equation

  1. Sep 24, 2012 #1
    T(z,t) = ∫ ( exp(-αz)* erfc(-α*sqrt((k*t)/(c*ρ))+0.5 sqrt((c*ρ*z)/(k*t)))*exp( -((t-ζ)/ζ0)^2)

    integrate with respect to ζ in the limits 0 and t

    Help will be greatly appreciated
  2. jcsd
  3. Sep 24, 2012 #2


    User Avatar
    Science Advisor

    I think you are letting complicated lookig constants confuse you.

    If I read the parentheses correctly that is
    [tex]\int (A+ 0.5\sqrt{Be^{-2(t- ζ)/ζ_0}})dζ[/tex]
    with A and B representing those rather complicated constants in your integral.
    I presume you know that [itex]\int Adt= At+ C[/itex]. For the second integral, let [itex]u= -2(t- ζ)/ζ_0[/itex], so that [itex]dζ= (ζ_0/2)du[/itex], so the second integral becomes
    [tex]B\frac{\zeta_0}{2}\int e^u du[/tex]
    Last edited by a moderator: Sep 24, 2012
  4. Sep 24, 2012 #3


    Staff: Mentor

    Fixed the LaTeX in the integral.
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