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I have a function Ca[t] that oscillates like a Sine curve, that I used NDSolve to obtain. I want to calculate the average value of Ca[t] so 1/2(Max+Min) but I have not been able to do this successfully and I don't know what to do. 

     Manipulate[

      k1 = 0.5; k2 = 0.2;
      r1 = -k1 Ca[t]^m;
      r2 = -k2 Cb[t]^n;
      xa = (Cao[0] - 
        0.5*(MaxValue[Ca[t], Reals] + MinValue[Ca[t], Reals]))/Cao[0];
      Cao[t_] = 5 + A Sin[ω t];
      sol = NDSolve[{
         Ca'[t] == r1*τ + -Ca[t] + Cao[t],
         Cb'[t] == r2*τ - r1*τ - Cb[t],
         Cc'[t] == -r2*τ - Cc[t],
         Ca[0] == 0,
         Cb[0] == 0,
         Cc[0] == 0},
        {Ca, Cb, Cc}, {t, 0, 100}];

   {{τ, 5, "residence time/min"}, 2, 10, Appearance -> "Labeled"},
   {{ω, 0.6, "frequency"}, 0.2, 2, 0.02, 
           Appearance -> "Labeled"},
   {{A, 2, "amplitude"}, 0.5, 5, 0.05, 
           Appearance -> "Labeled"},
   {{m, 1, "m"}, 0, 2, 1, ControlType -> SetterBar},
   {{n, 1, "n"}, 0, 2, 1, ControlType -> SetterBar}]

This is as much as I can trim my notebook, my latest attempt at calculating the average of Ca[t] inside the expression xa.

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Not very sophisticated but take a look:

Manipulate[k1 = 0.5; k2 = 0.2;
 r1 = -k1 Ca[t]^m;
 r2 = -k2 Cb[t]^n;
 Cao[t_] = 5 + A Sin[\[Omega] t];
 sol = Quiet@NDSolve[{
                     Ca'[t] == r1*\[Tau] + -Ca[t] + Cao[t], 
                     Cb'[t] == r2*\[Tau] - r1*\[Tau] - Cb[t], 
                     Cc'[t] == -r2*\[Tau] - Cc[t], Ca[0] == 0, Cb[0] == 0, 
                     Cc[0] == 0}, {Ca, Cb, Cc}, {t, 0, 100}];
 Framed@Row@{
  Plot[Evaluate[Ca[t] /. sol], {t, 0, 100}, ImageSize -> 600, Epilog -> {
       [email protected], Point[p = {t /. #2, #1} & @@@Quiet@(
       {FindMinimum[##], FindMaximum[##]} & @@ {Evaluate[Ca[t] /. sol], {t, 60}})]}
      ]
  ,
  "Average \[TildeTilde] ", Dynamic@N[Total[p[[All, 2]]]/2]
 }
 ,
 {{\[Tau], 5, "residence time/min"}, 2, 10, 
  Appearance -> "Labeled"}, {{\[Omega], 0.6, "frequency"}, 0.2, 2, 
  0.02, Appearance -> "Labeled"}, {{A, 2, "amplitude"}, 0.5, 5, 0.05, 
  Appearance -> "Labeled"}, {{m, 1, "m"}, 0, 2, 1, 
  ControlType -> SetterBar}, {{n, 1, "n"}, 0, 2, 1, 
  ControlType -> SetterBar}]

enter image description here

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  • $\begingroup$ Why are you solving for Cb and Cc? ... Ca[] isn't coupled! (r2 and n aren't needed, for a starter) $\endgroup$
    – Dr. belisarius
    Commented Jun 24, 2013 at 23:59
  • $\begingroup$ @belisarius Yes, of course. Well I didn't know what user7560 wants a the end, since sol is not scoped He can instatnly use it later. Also, it was not so demanding for my old pc so I left them. $\endgroup$
    – Kuba
    Commented Jun 25, 2013 at 5:04
  • $\begingroup$ @belisarius, they are necessary, I just left out the plots. Leaving them in there won't hurt anything for the purposes of this post. $\endgroup$
    – baumannr
    Commented Jun 25, 2013 at 14:42
  • $\begingroup$ @Kuba thank you for this, I am going to try this out! $\endgroup$
    – baumannr
    Commented Jun 25, 2013 at 14:42
  • $\begingroup$ @user7560 Next time try to post the minimal code snippet that demonstrates the behavior you need to clarify. $\endgroup$
    – Dr. belisarius
    Commented Jun 25, 2013 at 14:53

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