Re: Numerical integration

*To*: mathgroup at smc.vnet.net*Subject*: [mg73832] [mg73832] Re: Numerical integration*From*: dh <dh at metrohm.ch>*Date*: Fri, 2 Mar 2007 06:15:52 -0500 (EST)*References*: <es3iul$obt$1@smc.vnet.net>

Hi Dimitris, why do you want to calculate numerically an integral that can be done analytically? For a,b >1 we get: -(Pi (a - b + Abs[a - b])) -------------------------- 4 a (a - b) Daniel dimitris wrote: > In another post I talk about the integral > > Integrate[Cos[a x] CosIntegral[b x], {x, 0, Infinity}] > > I have problems to numerical integrate this function for say > {a,b}={3,2}. > > In[20]:= > Integrate[Cos[3*x]*CosIntegral[2*x], {x, 0, Infinity}] > N@% > > Out[20]= > -(Pi/6) > Out[21]= > -0.5235987755982988 > > No matter how I set Options I couldn't get satisfactory results by > NIntegrate. > > Any ideas will be greatly appreciate! > > Here is its plot > > In[59]:= > Plot[Cos[3*x]*CosIntegral[2*x], {x, 0, 10}, Ticks -> {Range[0, 10*Pi, > Pi/6], Automatic}] > > As we see the zeros if the function are situated at Pi/6 + n*(Pi/3), > n=0,1,2,3... > > In[61]:= > (Cos[3*#1]*CosIntegral[2*#1] & ) /@ Table[Pi/6 + n*(Pi/3), {n, 0, > 100}] > > Out[61]= > {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,\ > 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,\ > 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0} > > I tried to take use of this fact doing something like > > In[67]:= > lst = Table[Pi/6 + n*(Pi/3), {n, 0, 1000}] /. {a_, b__, c_} -> {x, 0, > a, b, c}; > > In[70]:= > NIntegrate[Cos[3*x]*CosIntegral[2*x], Evaluate[Sequence[lst]], > WorkingPrecision -> 40] > NIntegrate::ncvb :.... > -0.52359885758572151495786704 > > Very good result but I look for any other methods/settings! > > Dimitris > >