Error Analysis for Approximate Integration
Derrick Smith
1. Introduction
In kindergarten, when you first learned algebra, your teacher was happy if you could plug
into the formulas correctly.
At the college level, you should understand where the
formulas come from.
Overall your textbook does a good job deriving the formulas you
use, but does not give the intuition behind the error bounds for the various integral
approximation techniques.
The purpose of this supplement is to fill that gap.
2. First Error Bound for the Left Hand Rule and the Right Hand Rule
Suppose you wanted to approximate this area using the Left Hand Rule.
You would get a picture something like the one on the left in the diagram below. The
areas of the blue pieces are your approximation. Your error is the area of the gray regions.
Recall the algebraic formula for error: Error = (Actual Value – Approximation).
Draw the rectangles for the Right Hand Rule and scoot the yellow pieces off to the right.
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 Spring '10
 Williamson
 Derivative, Order theory, hand rule, Left Hand Rule, 2 2 K

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