🚀 go-pugleaf

From article <1992Aug28.011918.22579@harlow.harvard.edu>, by job@head-cfa.harvard.edu (Jeffrey Oliver Breen):
> In article <1992Aug14.040957.16304@Princeton.EDU> muyu@burn.Princeton.EDU (Muyu Guo) writes:
>>I am having trouble doing the integral using either qtrap
>>or qsimp from Numerical Recipes:
>>
>>    b
>>    /
>>    | f(x)dx,      	with a < 1, b > 2
>>    /
>>    a
>>   			and f(x) = 1 (1 <= x <= 2)
>>				 = 0  otherwise
>>
>>For example a=0, b=4 or the like the results were nonsense.
>>
>>Does anyone know if there is a good way to get thru this?
>>Thanks a million for your attention.
> 
> Since f(x) will be one from x=1 to x=2, and this range is included by
> the a<1 and b>2 guarantee, and the function is zero everywhere else,
> then the integral just becomes:
> 
>   2
>  /
>  | 1 dx, otherwise known as 1.  Is there a reason you were trying to
>  /
>  1
> 
> solve this numerically?
> -- 
> +-----------
> | Jeffrey Oliver Breen   Harvard-Smithsonian Center for Astrophysics,
> | (617) 495-7252         60 Garden St., Room B-340, MS 6, Cambridge, MA  02138
> |

I think I should rephrase the original question in the 
definition of f(x):   f(x) = 1 ( a < x1 < x < x2 < b)
			   = 0 otherwise

			   I don't know a prior what  is x1 and x2.

So I was told better use an adaptive algorithm for this. Actually
I can do it even with simple trap routine provided I don't want 
too much accuracy, say, relative error 1e-5 between successive
approximate values of the integral.

-- 
Muyu Guo