Approximate Integration: Trapezoidal Rule Error Bound: Proof

In this video I go over a very extensive proof of the Error Bound formula for the Trapezoidal Rule integration approximation method. In this video I derive an estimate of the error for a single sub-interval using the fact that the integration constant can be chosen to be any number (learn more about this in my next video so stay tuned!). From there I expand the estimate and sum it up for all n-intervals. Now selecting the number K to be at least the maximum value of the absolute value of the second derivative for the given interval, I am able to derive the maximum error bound estimate. In the video I also explain how there are some significant weaknesses in the derivation and show that the actual error can be much less than the maximum error bound estimate. This is a very long and extensive example but it will give you a profound understanding of mathematics and integral approximations in general so make sure to watch the video and follow along if you can!

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Related Videos:

Approximate Integration: Accuracy and Error Bounds: http://youtu.be/WTdNktL_1Uc Approximate Integration: Example 1: 1/x: http://youtu.be/DTzZ1jz6OOg Approximate Integration: Left, Right, Midpoint, and Trapezoidal Rules: http://youtu.be/zWzmaLvQU6w The Definite Integral - Brief Introduction: http://youtu.be/vhMP5SKbQjU Evaluating Integrals - Examples Part 1 - Using Infinite Rectangles: http://youtu.be/cvqH43bRLoE Evaluating Integrals - Examples Part 2 - Interpreting as Areas: http://youtu.be/yRP_7umJmIo Evaluating Integrals - Midpoint vs Right Endpoint Approximations Comparison: http://youtu.be/3x3sF7P9xfY Completing the Square: http://youtu.be/5uxV6-f_qc0 .

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