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## Trapezoid Rule |

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z | overview |

The approximation

refers to the integral as a sum of trapezoids.

For a twice continuously differentiable function, the error can be estimated via

with .

More precisely, the error for smooth functions bears the asymptotic expansion

with constants independent from and . Thus the trapezoid rule is very exact for -periodic functions. The error strives faster towards zero than any -potence.

(Authors: Höllig/Hörner/Abele)

**Annotation:**

- Beweis: Fehler der Trapezregel (german)

automatically generated 4/ 7/2008 |