On Monday 14 April 2003 14:26, Felix E. Klee wrote:
> Thank you. This seems to work very well even for more complicated
> integrands and for integration over singularities (note that I haven't
> verified my results yet).
Hm, the results I got aren't correct. For example
ldefint(1/(cos(x)+sin(x)+10),x,0,2*%pi);
returns 0 while
romberg(1/(cos(x)+sin(x)+10),x,0,2*%pi);
returns 0.63. Maybe it isn't correct to use LDEFINT to integrate over
singularities. Am I doing something wrong or is this a bug?
> Maxima really seems to be very powerful when it comes to integration. I
> guess I need to RTFM to get accustomed to all these features. Only if the
> documentation were better, e.g. in the info pages I find
>
> - Function: DEFINT (exp, var, low, high)
> DEFinite INTegration, the same as INTEGRATE(exp,var,low,high).
>
> But this is unaccurate: as you showed above, integrate and defint are not
> identical (they are of course identical from the mathematical point of
> view).
Oh, oh, I must have overlooked the "L" above. If I just apply DEFINT to the
expressions in question it really behaves as integrate (i.e. it returns the
integral unevaluated). So the documentation seems to be correct.
Felix
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