Question

What is Integration Using the Trapezoidal Rule?

Answer 1

Let us divide the interval `[a,b]` into n subintervals of equal lengths.

`[a,b] to {[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`.

We can approximate the definite integral

`int_a^b f(x)dx`

by Trapezoid Rule

`T_n=[f(x_0)+2f(x_1)+2f(x_2)+cdots2f(x_{n-1})+f(x_n)]{b-a}/{2n}`