Question

How do you Use the trapezoidal rule with four equal subdivisions to approximate a definite integral?

Answer 1

First split the interval `[a,b]` into 4 equal subintervals:

`[x_0,x_1],[x_1,x_2],[x_2,x_3]`, and `[x_3,x_4]`.

(Note: `x_0=a` and `x_4=b`)

The definite integral

`int_a^b f(x)dx`

can be approximated by

`T_4=[f(x_0)+2f(x_1)+2f(x_2)+2f(x_3)+f(x_4)]cdot{Delta x}/{2}`,

where `Delta x={b-a}/4`.

I hope that this is helpful.