Test Problem.

Use your routines to compute the Gaussian integral

whose value (computed with 14 accurate digits) is shown above.

The results are given below.

SINGLE PRECISION
Tol	Trapezoidal		Simpson
	error	n	error	n
0.1E+01	-.2E-01		0.5E-03
0.1E+00	-.2E-01		0.4E-04
0.1E-01	-.1E-02		0.4E-04
0.1E-02	-.3E-03		0.4E-04
0.1E-03	-.2E-04		0.3E-05
0.1E-04	-.1E-05		0.2E-06
0.1E-05	-.2E-06		-.8E-07
0.1E-06	-.2E-06		0.0E+00
0.1E-07	-.1E-04		0.8E-07
0.1E-08	-.1E-04		0.8E-07
0.1E-09	-.1E-04		0.8E-07
0.1E-10	-.1E-04		0.8E-07
0.1E-11	-.1E-04		0.8E-07

DOUBLE PRECISION
TOL	Trapezoidal		Simpson
	error	n	error	n
0.1E+01	-.2E-01		0.5E-03
0.1E+00	-.2E-01		0.4E-04
0.1E-01	-.1E-02		0.4E-04
0.1E-02	-.3E-03		0.4E-04
0.1E-03	-.2E-04		0.3E-05
0.1E-04	-.1E-05		0.2E-06
0.1E-05	-.3E-06		0.1E-07
0.1E-06	-.2E-07		0.7E-09
0.1E-07	-.1E-08		0.7E-09
0.1E-08	-.3E-09		0.4E-10
0.1E-09	-.2E-10		0.3E-11
0.1E-10	-.1E-11		0.2E-12
0.1E-11	-.3E-12		0.6E-14

Aside from the project, compare the results above with thre results obtained via Gaussian Quadrature integration formula. This method gives excellent results with only several node points; it is therefore much more efficient than both trapezoidal and Simpson rules.

Gauss Quadrature
error	n
-3.0E-4	2
-1.2E-5	3
4.4E-7	4
-8.0E-9	5