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Solve equation comprising integration and giving the value of constants?

Posted 2 months ago
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Consider the following code:

NDSolve[(α*P)/(Pi*ρ*Cp)*Integrate[Exp[-2 ((x - V t)^2 + z^2)/(8 Qt + ω^2)], {t, 0, Infinity},x == 0, α == 4, ρ == 789, Cp== 2440, P == 0.04, Q == 0.0000000883, ω == 0.00035, V == 2, z == 1] 

I have used this to solve the equation with the values of constants given here. I am getting an error of "Integrate: Invalid integration variable or limit(s) in x==0". What am I doing wrong here?

x = 0; α = 4; ρ = 789; Cp = 2440; P = 1/25; Qt = 883/10000000000; ω = 7/20000; V = 2; z = 1;
(α*P)/(Pi*ρ*Cp)*Integrate[Exp[-2 ((x - V t)^2 + z^2)/(8 Qt + ω^2)], {t, 0, Infinity}]

(* Sqrt[921/(2 π)]/(1604300000000 E^(20000000000/8289)) *)

N[%, 100](* By numerics *)
(* 2.46422625741300841899845719658810928889079877714383973615143785469577\
3747025826659955337739134874899*10^-1047893 *)
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