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Q: Tough Calculus Integration Problem ( No Answer,   1 Comment )
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
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.

most  diff. eq. of the type you have do not usually have an analytical solution.
There is no answer at this time.

Subject: Re: Tough Calculus Integration Problem
From: cw4ever-ga on 17 Jul 2006 11:17 PDT
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.

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