Integration Using the Trapezoidal Rule
Key Questions

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_{n1},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_{n1})+f(x_n)]{ba}/{2n}# .
I hope that this was helpful.

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={ba}/4# .I hope that this is helpful.

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_{n1},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_{n1})+f(x_n)]{ba}/{2n}#