Midpoint vs Trapezoid Rule Error
- Author:
- Eugene Yablonski, Bill Scott
- Topic:
- Trapezoid
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)