How to integrate this equation

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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
 

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  • #2
HallsofIvy
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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]
 
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  • #3
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Fixed the LaTeX in the integral.
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]
 

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