Question

How does the trapezoidal rule work?

Answer 1

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}`.

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I hope that this was helpful.