How does the trapezoidal rule work?

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Answer 1 · 2014-10-17T01:45:37

Let us approximate the definite integral

$int_a^b f(x)dx$

by Trapezoid Rule $T_n$ .

First, split the interval $[a,b]$ into $n$ equal subintervals:

$[x_0,x_1], [x_1,x_2],[x_2,x_3],...,[x_{n-1},x_{n}]$ ,

where $a=x_0 < x_1 < x_2< cdots < x_n=b$ .

Trapezoid Rule $T_n$ can be found by

$T_n=[f(x_0)+2f(x_1)+2f(x_2)+cdots+2f(x_{n-1})+f(x_n)]{b-a}/{2n}$ .

I hope that this was helpful.