Q000001: Gauss–Legendre

Alternative namesGauss
Integral\(\displaystyle \int f(x)\,\mathrm{d}x\)
NotesIf \(f(x)\) is a degree \(2n-1\) polynomial, then an order \(n\) Gauss–Legendre rule will integrate it exactly.
References
Gauss, Carl Friedrich. Methodus nova integralium valores per approximationem inveniendi, Werke, 165–196, 1866. [DOI: 10.1017/CBO9781139058247.008]

Interval

Order 1

↓ show points and weights ↓

Order 2

↓ show points and weights ↓

Order 3

↓ show points and weights ↓

Order 4

↓ show points and weights ↓

Order 5

↓ show points and weights ↓
View higher order rules