# Some trivial but confusing terms about numerical integration

Some terminological questions about numerical integration:

1. When a question states trapezoidal rule with 2 points, does that mean 2 subintervals or 3 subintervals? Since 3 subintervals have 2 points other than the end points.

2. How about a Gaussian rule with 2 quadrature points? Does that mean when $n=2$? So the integral can be approximated by $$\sum_{i=0}^{2}A_if(x_i)=A_0f(x_0)+A_1f(x_1)+A_2f(x_2)$$ But then there will be 3 $x_i$'s? Which means there are "3 points"? Or does "Gaussian rule with 2 points" mean $n=1$?

Thanks for the clarification.

• Two points = one interval – fosho Apr 26 '16 at 11:35

1) The trapezoidal rule uses two points, the endpoints of a single interval, whereas the composite trapezoidal rule, is the extention of the trapezoidal rule to $N$ subintervals. These are typically, but not necessarily, back-to-back and so there are (typically) N+1 relevant nodes.
2) A Gaussian rule with two nodes is of form $A_0 f(x_0) + A_1 f(x_1)$. Your example has three nodes.