Computes "progressive" values
of the numerical integral, Y(x) =
∫ax
f(t) dt, for a ≤ x ≤ b,
by the selected method of integration, trapezoidal or
Simpson's rule. The function f is chosen from:
| | f(x) |
Integral, I | Result |
Reference |
| A) | 1⁄(1 + x²) |
arctan(x) | I(1, 4) = 0.5404195... |
[Atkinson, 1985, p 160] |
| B) | x ln x |
(1⁄4) x² (2 ln x − 1) |
I(1, 2) = 2 ln 2 − 1 + 1 ⁄ 4 = 0.63629436... |
[Conte & de Boor, 1980, p 327] |
| C) | √x |
(2⁄3) x^(3⁄2) |
I(1, 4) = 4 2⁄3 = 4.(6) |
[Scheid, 1991, p 159] |
† If n is not a multiple of npr,
the former is adjusted (increased).
Curves are drawn for the numerical, Ynum,
and analytical, Yan, integrals
(usually indistinguishable), and their difference (error). |
• Weisstein, Eric W. "Numerical
integration". From MathWorld—a Wolfram web resource.
• Wolfram Mathematica
Online Integrator.
• Atkinson, Kendall,
1985, "Elementary numerical analysis",
John Wiley & Sons, New York, NY (USA).
ISBN 0-471-82983-8.
• Conte, Samuel D., and
Carl de Boor,
1980 (1987), "Elementary numerical analysis",
McGraw-Hill, Singapore.
ISBN 0-07-066228-2.
• Scheid, Francis,
1991, "Análise Numérica",
McGraw-Hill de Portugal, Lisboa (Portugal).
ISBN 972-9241-19-8.
• Greenspan, Donald,
Vincenzo Casulli,
1988, "Numerical analysis
for applied mathematics, science, and engineering",
Addison-Wesley, Redwood City, CA (USA).
ISBN 0-201-09286-7 (QA297.G725).
• Search numerical integration...
• Numerical methods (bibliography: "Eric's Scientific Book List").
• Euclidean
algorithm for gcd (lcm) (Wikipedia).
• 1830-12-07: Cremona, Antonio Luigi Gaudenzio Giuseppe
(1903-06-10). |
