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