7dot7ErrorAnalysis - Error Analysis for Approximate...

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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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This note was uploaded on 04/12/2011 for the course CALC 215 taught by Professor Williamson during the Spring '10 term at Grand Valley State University.

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7dot7ErrorAnalysis - Error Analysis for Approximate...

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