Solving an integration problem at specific time points

Hello,

I am interested in solving this equation below where I have specific time points that correlate with a gp value. I need to solve the integral at specific time points and multiplying that answer with the rest of the equation that also depends on time. In the end, I want to plot how hp2 looks from 0 to 480 at those time points.

I'm not sure how to have the answer of the integral at a specific time point and then use that same time point for the equation outside of the integral.

Any help is greatly appreciated. Thank you.

t = [0 30 60 90 120 180 240 300 360 420 480];
gp = [10.75 9.45 7.963 5.15 7.213 6.725 6.525 6.325 5.988 5.475 5.213];

Rm = 4.44.*(10.^-12);
b1 = 0.0151;
b2 = 0.002;
q2 = 1.85;
alpha2 = 0.01594;
C1 = 1162;
hp2 = 5.38*(10^-10); %hp2(0)

%-------------------------------------------------------------------------%
syms s

for n = 1:11
    disp(gp(n))
    disp(t(n))
    eqn = (Rm.*exp(-(b1+b2).*s))./(1+(q2.*exp(alpha2.*(C1-gp(n)))));
    Fint = int(eqn,s,[0 t(n)]);
    Fvpa = vpa(Fint);
    
    fiteqn = ((exp((-b1+b2).*t(n)).*hp2))+((exp((-b1+b2).*t(n))).*Fvpa);
    
    figure(1)
    plot(t,fiteqn)
    endend

Answer 1

[Dinesh Yadav]

Hi, The issue here is vpa gives a symbolic output, to use it with a function like plot,there is a need to convert the output of vpa to lets say double that can be used with plot as t is also of type double by default. I am attaching the file with few changes to your code.

Hope it Helps.