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Q: Tough Calculus Integration Problem ( No Answer,   1 Comment ) Question
 Subject: Tough Calculus Integration Problem Category: Science > Math Asked by: spoonman-ga List Price: \$100.00 Posted: 13 Jul 2006 12:22 PDT Expires: 12 Aug 2006 12:22 PDT Question ID: 746028
 ```I would like to integrate the following equation. It is a chemical rate equation (Arrhenius) where I have temperature & relative humidity as functions of time. Both are sinusoidal, reflecting a typical yearly climate: e^-(Integral(k*RH(t))dt), where k=Ae^-(E/R*T(t)) and RH(t) = 0.7+0.1*Sin(0.01t), T(t) = 300+4.5*Sin(0.01t).``` Request for Question Clarification by hedgie-ga on 20 Jul 2006 08:25 PDT ```It is fairly simple to integrate that numerically. Do you want help with that as an answer? Or does 'integrate' means :find an analytical solution (which does not exist)?``` Clarification of Question by spoonman-ga on 31 Jul 2006 09:47 PDT ```In response to hedgie-ga, I was hoping to arrive at an equation which I could then graph to show the reaction rate as a function of time (given the input temperature, and relative humidity equations). Sorry, I don't understand what you mean by integrate numberically? Does this mean that you would achieve a numerical result given integration limits? If so, that's not of particular use to me.``` Request for Question Clarification by hedgie-ga on 31 Jul 2006 11:20 PDT ```In numerical solution you do not obtain an equation, but rather a table You can still plot it vs time. http://www.myphysicslab.com/numerical_vs_analytic.html most diff. eq. of the type you have do not usually have an analytical solution.```  ```As a matter of significance, you ought to be able to take T(t) = 300. That is, given your numerical constants, your solution will only have one significant digit anyway. Letting T(t) = 300 yields: exp[-A*exp(-E/(300*R))*(0.7*t-10*cos(0.01t))] If this is unacceptable, there are other approximations you may be able to make. However, I doubt it can be solved exactly.``` 