NIntegrate Confusion

• To: mathgroup at smc.vnet.net
• Subject: [mg109158] NIntegrate Confusion
• From: sukhrob <suhrob84 at bk.ru>
• Date: Wed, 14 Apr 2010 05:16:26 -0400 (EDT)

```Hi everybody,
I'm using Mathematica 7.0 , i would like integrate numerically something
like Fourier coefficients, my programe code contains:

M = 50; f[t_] = 100 Sin[5 t];

basis = Table[Sin[n t], {n, 1, M}];

coef = 2/Pi*Table[NIntegrate[f[t] Sin[n t], {t, 0, Pi}], {n, 1, M}]

in result it gives :

NIntegrate::ncvb: NIntegrate failed to converge to prescribed accuracy after
9 recursive bisections in t near {t} = {2.47283}. NIntegrate obtained
-3.88578*10^-15 and 7.654706546923104`*^-15 for the integral and error
estimates. >>
NIntegrate::ncvb: NIntegrate failed to converge to prescribed accuracy after
9 recursive bisections in t near {t} = {2.47283}. NIntegrate obtained
-3.19189*10^-15 and 1.8799124112361456`*^-14 for the integral and error
estimates. >>

NIntegrate::ncvb: NIntegrate failed to converge to prescribed accuracy after
9 recursive bisections in t near {t} = {0.00254055}. NIntegrate obtained
1.2045919817182948`*^-14 and 9.105942246869344`*^-13 for the integral and
error estimates. >>

General::stop: Further output of NIntegrate::ncvb will be suppressed during
this calculation. >>

Can anyone help me to solve  that problem. Any help would be very much
appreciated.