## You are here

Homequadrature

## Primary tabs

# quadrature

*Quadrature* is the computation of a univariate definite integral. It can refer to either numerical or analytic techniques; one must gather from context which is meant. The term refers to the geometric origin of integration in determining the area of a plane figure by approximating it with squares.

*Cubature* refers to higher-dimensional definite integral computation. Likewise, this term refers to the geometric operation of approximating the volume of a solid by means of cubes (and has since been extended to higher dimensions).

The terms “quadrature” and “cubature” are typically used in numerical analysis to denote the approximation of a definite integral, typically by a suitable weighted sum. Perhaps the simplest possibility is approximation by a sum of values at equidistant points, i.e. approximate $\int_{0}^{1}f(x)\,dx$ by $\sum_{{k=0}}^{n}f(k/n)/n$. More complicated approximations involve variable weights and evaluation of the function at points which may not be spaced equidistantly. Some such numerical quadrature methods are Simpson’s rule, the trapezoidal rule, and Gaussian quadrature.

## Mathematics Subject Classification

28-00*no label found*65D32

*no label found*41A55

*no label found*26A42

*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff

## Recent Activity

new question: Prove that for any sets A, B, and C, An(BUC)=(AnB)U(AnC) by St_Louis

Apr 20

new image: information-theoretic-distributed-measurement-dds.png by rspuzio

new image: information-theoretic-distributed-measurement-4.2 by rspuzio

new image: information-theoretic-distributed-measurement-4.1 by rspuzio

new image: information-theoretic-distributed-measurement-3.2 by rspuzio

new image: information-theoretic-distributed-measurement-3.1 by rspuzio

new image: information-theoretic-distributed-measurement-2.1 by rspuzio

Apr 19

new collection: On the Information-Theoretic Structure of Distributed Measurements by rspuzio

Apr 15

new question: Prove a formula is part of the Gentzen System by LadyAnne

Mar 30

new question: A problem about Euler's totient function by mbhatia

## Corrections

Quadrature by tensorking ✓

Classification by archibal ✓

quadrature and cubature by igor ✓

Formula by Mravinci ✓