Quadratur von Christian Buth
(c) 2000 Christian Buth

Quadratur von k(x) mit der Trapezregel:
N = 1       I = 2                  errI = 1.14e+00
N = 2       I = 2.732050807569     errI = 4.10e-01    alpha = 1.5
N = 4       I = 2.995709068102     errI = 1.46e-01    alpha = 1.5
N = 8       I = 3.089819144357     errI = 5.18e-02    alpha = 1.5
N = 16      I = 3.123253037828     errI = 1.83e-02    alpha = 1.5
N = 32      I = 3.135102422877     errI = 6.49e-03    alpha = 1.5
N = 64      I = 3.13929691278      errI = 2.30e-03    alpha = 1.5
N = 128     I = 3.140780792397     errI = 8.12e-04    alpha = 1.5
N = 256     I = 3.141305582957     errI = 2.87e-04    alpha = 1.5
N = 512     I = 3.14149115272      errI = 1.02e-04    alpha = 1.5
N = 1024    I = 3.141556766539     errI = 3.59e-05    alpha = 1.5

Quadratur von k(x) mit der Simpsonregel:
N = 1       I = 2.976067743425     errI = 1.66e-01
N = 2       I = 3.083595154947     errI = 5.80e-02    alpha = 1.5
N = 4       I = 3.121189169775     errI = 2.04e-02    alpha = 1.5
N = 8       I = 3.134397668985     errI = 7.19e-03    alpha = 1.5
N = 16      I = 3.139052217894     errI = 2.54e-03    alpha = 1.5
N = 32      I = 3.140695076081     errI = 8.98e-04    alpha = 1.5
N = 64      I = 3.141275418936     errI = 3.17e-04    alpha = 1.5
N = 128     I = 3.141480513144     errI = 1.12e-04    alpha = 1.5
N = 256     I = 3.141553009307     errI = 3.96e-05    alpha = 1.5
N = 512     I = 3.141578637812     errI = 1.40e-05    alpha = 1.5
N = 1024    I = 3.141587698369     errI = 4.96e-06    alpha = 1.5

Quadratur von f(x) mit der Trapezregel:
N = 1       I = 3                  errI = 1.42e-01
N = 2       I = 3.1                errI = 4.16e-02    alpha = 1.8
N = 4       I = 3.131176470588     errI = 1.04e-02    alpha = 2
N = 8       I = 3.138988494491     errI = 2.60e-03    alpha = 2
N = 16      I = 3.140941612041     errI = 6.51e-04    alpha = 2
N = 32      I = 3.141429893175     errI = 1.63e-04    alpha = 2
N = 64      I = 3.141551963486     errI = 4.07e-05    alpha = 2
N = 128     I = 3.141582481064     errI = 1.02e-05    alpha = 2
N = 256     I = 3.141590110458     errI = 2.54e-06    alpha = 2
N = 512     I = 3.141592017807     errI = 6.36e-07    alpha = 2
N = 1024    I = 3.141592494644     errI = 1.59e-07    alpha = 2

Quadratur von f(x) mit der Simpsonregel:
N = 1       I = 3.133333333333     errI = 8.26e-03
N = 2       I = 3.141568627451     errI = 2.40e-05    alpha = 8.4
N = 4       I = 3.141592502459     errI = 1.51e-07    alpha = 7.3
N = 8       I = 3.141592651225     errI = 2.36e-09    alpha = 6
N = 16      I = 3.141592653553     errI = 3.70e-11    alpha = 6
