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).

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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)?

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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.

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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.