Re: [Help-gsl] Can you do this in GSL?

[ake]

At 08:13 PM 1/17/2005, Kenneth Geisshirt wrote:

> > I wrote the integral wrong. Sorry! The correct function is:
> > 0.067*b^3 = \int_0^b x^2/(exp(x)+1) dx

> Assume that F(b) = \int_0^b x^2/(exp(x)+1) dx. Your equation is then 
> 0.067*b^3 = F(b) - F(0) = F(b). Now differentiate wrt b, and you have 
> 0.2*b^2 = F'(b) = f(b).

Since this is an equation it does not hold for every b and consequently you 
cannot differentiate both sides and retain equality. Example: b^2 = 1 has 
two possible solutions, b = 1 and b = -1. If you incorrectly differentiate 
both sides wrt b you get 2*b = 0, thus b = 0.

> You can calculate f(b) as a finite difference, f(b) = (F(b+h)-F(b-h))/2h. 
> In general you can calculate F(b) using an integration function found in 
> GSL. Last, your solve the equation G(b) = f(b)-0.2*b^2 = 0 using a 
> nonlinear equation solver in GSL.

If, for some reason, you would like to find f(b) = F'(b) the fundamental 
theorem of calculus would tell you immediately that f(b) = b^2/(exp(b)+1). 
You could then solve f(b) = 0.2*b^2 by hand.

Regards,
Åke