Re: numeric integration

*To*: mathgroup at smc.vnet.net*Subject*: [mg81158] Re: numeric integration*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Fri, 14 Sep 2007 03:37:00 -0400 (EDT)*Organization*: The Open University, Milton Keynes, UK*References*: <fcb40h$fm3$1@smc.vnet.net>

C. Seja wrote: > I'd like to intergate a function f with NIntegrate: > NIntegrate[f[x], {x, 0, 0.1}] > > But this doesn't work if, i.e. > > f = NIntegrate[Sin[x + #], {x, 0, 1}] & > > It will give a wrong result (0.7 instead of 0.05). Why? I mean, I can > evaluate f at any point without problems, i.e. f[0.1] gives 0.37. In[1]:= f = NIntegrate[Sin[x + #], {x, 0, 1}] &; f[0.1] Out[2]= 0.541408 > So why doesn't > > NIntegrate[f[x], {x, 0, 0.1}] > > work? It doesn't even give a warning! So, is there a proper way to do this > (without using one two-dimensional NIntegrate)? In[1]:= f[y_?NumericQ] := NIntegrate[Sin[x + y], {x, 0, 1}] In[2]:= f[0.1] Out[2]= 0.541408 In[3]:= NIntegrate[f[y], {y, 0, 0.1}] Out[3]= 0.050097 Regards, -- Jean-Marc