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

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Answer 1 · 2014-09-28T01:12:20

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.