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

[zkoza]

>>    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 with b, and you have 0.2*b^2 = F'(b) = f(b).

> You can calculate f(b) as a finite difference, f(b) = (F(b+h)-F(b-h))/2h.

You can do even better: since b is used only as the upper limit in the 
integral, the derivative is simply the integrand:
f(b) = b^2/(exp(b)+1).
After substituting it to 0.2*b^2 = f(b), you are left with
something as simple as exp(b) \approx 4, or 
b \approx ln(4).

regards,
Z. Koza