II. Midpoint Rule

Let M (midpoint) =and f(m) is given

 

I = f(m)*(b-a)

Here we have only: w₁x₁⁰ = w₁x_m⁰ = b-a  w₁ = b-a

I =

Taylor Series Method:

Alternatively, expand f(x) about m, then:

 

f(x) =
 

I =

Error in integration, using midpoint rule, is: 0(b-a)³