Newton-Cotes Quadrature Formulas

​
type of formula
closed
open
subdivisions
1
2
3
4
5
endpoint b
11π
6
Newton-Cotes formula:
3
8
h(f(
x
0
)+3f(
x
1
)+3f(
x
2
)+f(
x
3
))
integral:
approximated value = 0.281295
actual value = 0.133975
error = 0.14732
This Demonstration shows the Newton–Cotes quadrature formulas of integration and their application to the integration of
sin(x)
.
The Newton–Cotes integration formulas are just the integrals of interpolating polynomials.
The Newton–Cotes formulas may be "closed" if the endpoints
x
0
and
x
n
are used to obtain the interpolating polynomial.
The Newton–Cotes formulas are "open" if the extremes of the interval
[a,b]
are not used to obtain the interpolating polynomial.

External Links

Newton (Wolfram MathWorld)

Permanent Citation

Eugenio Bravo Sevilla
​
​"Newton-Cotes Quadrature Formulas"​
​http://demonstrations.wolfram.com/NewtonCotesQuadratureFormulas/​
​Wolfram Demonstrations Project​
​Published: January 17, 2008