----------------
#  Aufgabe 2b  #
----------------

hochzahl = (-8):8
r = 10^hochzahl
r                    # wir nehmen 10^(-8) bis 10^8 = 100 Mio

n = 100000
phi = seq(from=0,to=pi,length=n)

for(rr in r)
{
  z = rr*exp(1i*phi)  
  dz = diff(z)
  z = z[-1]
  fz = exp(1i*z)/z
  result = sum( fz*dz )
  print(result)
}


# checken wir noch das reelle Integral 
# int_{-infty}^{infty} sin(x)/x

xmax = 10000
x = seq( from=-xmax, to=xmax, by=0.001 )
dx = diff(x)
x = x[-1]
fx = ifelse( x^2>0 , sin(x)/x , 1 )
sum( fx*dx )