Midpoint vs Trapezoid Rule Error

1. Note that when you rotate the line through the midpoint, the area under that line does not change. 2. When point D is very close to point C, then (Error in the Trapezoid Rule )+2*(Error in the Mid-point Rule) 0. Thus, we can reduce the error by taking the weighted average: Simpson's Approximation (Trapezoid Approximation )+(Mid-point Approximation)