Wave Propagation in Linear Media | re-examined

In[23]:= f[x_] := Exp[-x] Cos[x];
OscInt[f,#&,0]
Out[23]= 0.5
7 Mathematica implementation of a quadrature function
In this case we do not even have the slightest approximation error, as can be shown by the attempt
to reveal further digits of the result.
In[24]:= SetPrecision[%,40]
Out[24]= 0.5
Example 7.5.7
Z 1
0
x
x 2 +1 sin xdx = 2e
In[25]:= f[x_] := x/(x^2+1) Sin[x];
SetPrecision[OscInt[f,#&,0],16] - N[Pi/(2 E),20]
Out[25]= -14
-1.93 10
Example 7.5.8
Z 1
0
cos x
p x 2 +1 dx = K0(1)
In[26]:= f[x_] := Cos[x]/Sqrt[x^2+1];
SetPrecision[OscInt[f,#&,0],16] - N[BesselK[0,1]]
Out[26]= -13
-1.12188 10
Example 7.5.9
Z 1
0
ln x2 +4
x2 +1 cos !x dx = , ,! ,2!
e , e
!
In[27]:= f[x_] := Log[(x^2+4)/(x^2+1)] Cos[omega x];
omega = 5;
SetPrecision[OscInt[f,omega #&,0],16] -
N[(Exp[-omega]-Exp[-2 omega]) Pi/omega,20]
184