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.