The discussion centers on integrating the complex equation 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) with respect to ζ from 0 to t. Participants clarify the integration process by breaking down the equation into simpler components, specifically identifying constants A and B. They emphasize the importance of correctly interpreting the limits and applying substitution methods, such as letting u = -2(t-ζ)/ζ0, to facilitate the integration of the exponential term.
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HallsofIvy said:If I read the parentheses correctly that is
\int (A+ 0.5\sqrt{Be^{-2(t- ζ)/ζ_0}})dζ
with A and B representing those rather complicated constants in your integral.
I presume you know that \int Adt= At+ C. For the second integral, let u= -2(t- ζ)/ζ_0, so that dζ= (ζ_0/2)du, so the second integral becomes
B\frac{\zeta_0}{2}\int e^u du