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MathGroup Archive 1997

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Re: Integration

  • To: mathgroup at smc.vnet.net
  • Subject: [mg5933] Re: [mg5865] Integration
  • From: Daniel Lichtblau <danl>
  • Date: Tue, 4 Feb 1997 00:04:21 -0500
  • Organization: Wolfram Research, Inc.
  • Sender: owner-wri-mathgroup at wolfram.com

Mark Dowell wrote:
>
> I have a question involving the definite INTEGRATE function.
> With integration you give Mathematica; the function of x, and the values of
> x between which you want it integrated.  My problem is that I KNOW the area
> I want (and know that I am using the origin as xmin) but I need Mathematica
> to calculate xmax for me.
> In words my equation is:
> CHLstep = the integral (with respect to x) of the function CHLfunc(between 0
> and certain value of x)
>
> Where what I need is what value of x will make that statement true. (CHLstep
> is a fraction.)
>
> Thanks
> Mark
> Mark Dowell                                     Ispra, I-21020, (VA)
> Marine Environment Unit TP 272                  Italy.
> Space Applications Institute                    E-mail: mark.dowell at jrc.it
> Joint Research Centre                           Talk: dowell at biscay.jrc.it
> Ispra Site                                      Phone: +39-332-789873
> Commission of the European Communities          Fax: +39-332-789034
>
>


If the indefinite integral can be computed, you can do

f[x] = Integrate[g[x], x]

Assuming no bad discontinuities, that is, definite integral is equal to
evaluated indefinite integral, you then simply do

Solve[f[xmax]-f[0]==area, xmax]

If you cannot get the indefinite integral, you might try approaching
this problem numerically. Using NIntegrate and various upper bounds,
subdivide the region in which you place a trial xmax until it gives an
integral sufficiently close to the area.

Daniel Lichtblau
Wolfram Research


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