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

Sep 28, 2014

First split the interval $\left[a , b\right]$ into 4 equal subintervals:

$\left[{x}_{0} , {x}_{1}\right] , \left[{x}_{1} , {x}_{2}\right] , \left[{x}_{2} , {x}_{3}\right]$, and $\left[{x}_{3} , {x}_{4}\right]$.

(Note: ${x}_{0} = a$ and ${x}_{4} = b$)

The definite integral

${\int}_{a}^{b} f \left(x\right) \mathrm{dx}$

can be approximated by

${T}_{4} = \left[f \left({x}_{0}\right) + 2 f \left({x}_{1}\right) + 2 f \left({x}_{2}\right) + 2 f \left({x}_{3}\right) + f \left({x}_{4}\right)\right] \cdot \frac{\Delta x}{2}$,

where $\Delta x = \frac{b - a}{4}$.

I hope that this is helpful.