It is a Quadrature where the domain x∈[a,b] is split into multiple grid points j=0,1,2…J with a=x0<x1<⋯<xJ=b
∫abf(x)dx=j=0∑J−1∫xjxj+1f(x) dx
We sum only till (J−1) because j=J is the end point which means the substitution xJ+1 doesn’t exist.
Example
Quadrature rule | Composite Quadrature | Fixed Step |
---|
Left Rectangle | ∑j=0J−1f(xj)(xj+1−xj) | h∑j=0J−1f(xj) |
| | |
Midpoint | ∑j=0J−1f(2xj+1+xj)(xj+1−xj) | h∑j=0J−1f(2xj+1+xj) |
| | |
Trapezoid | ∑j=0J−1(xj+1−xj)2f(xj)+f(xj+1) | 2h∑j=0J−1(f(xj)+f(xj+1)) |
Simpson’s | | 6h∑j=0J−1(f(xj)+4f(2xj+xj+1)+f(xj+1)) |