# How to create an integral function? Trying to solve Cp_b between 2 numbers

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Skye Cameron on 22 Feb 2020
Commented: madhan ravi on 22 Feb 2020
%%Calculate Benzene Duty Q
%From Perry's table 2-153 values for Benzene
C1_b = 162940; %in J/kmol*K
C2_b = -344.94; %in J/kmol*K^2
C3_b = 0.85562; %in J/kmol*K^3
funcCp_b = @(T) (C1_b) + (C2_b*T) + (C3_b*T^2);
Cp_b = int(funcCp_b,T, 379.25, 286.15)

madhan ravi on 22 Feb 2020
Edited: madhan ravi on 22 Feb 2020
clear all
%%Calculate Benzene Duty Q
%From Perry's table 2-153 values for Benzene
C1_b = 162940; %in J/kmol*K
C2_b = -344.94; %in J/kmol*K^2
C3_b = 0.85562; %in J/kmol*K^3
funcCp_b = @(T) (C1_b) + (C2_b*T) + (C3_b*T.^2);
Cp_b = integral(funcCp_b, 379.25, 286.15)

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Skye Cameron on 22 Feb 2020
I have this at the end, i do not understand why this isnt working also? Trying to solve for T2
syms T2
TempCumene = vpasolve ((((281.4749/3600)*Cp_b)*(T2-414.95) = Q_b),T2) %temp for cumene outlet in K
madhan ravi on 22 Feb 2020
The answer I get is
Cp_b = -1.3360e+07
madhan ravi on 22 Feb 2020
As the error message says use == Q_b