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Approximate Integration: Accuracy and Error Bounds

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First published at 07:11 UTC on July 29th, 2019.

#mathematics
#calculus
#science

Math Easy Solutions

MES

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In this video I revisit the example I went over in my last video on approximate integration and this time compare the accuracy of the different approximation methods as well as discuss a bit about the error bounds estimate formulas for the trapezoidal and midpoint rules. The example I go over is approximating the integral of the function 1/x from x = 1 to x = 2. I go over some very useful observations in the error comparisons between the Left, Right, Trapezoidal, and Midpoint Rule approximation methods as well as seeing how the error diminishes with increased number of sub-intervals. Also, I show in detail why for most cases, the Midpoint Rule is much more accurate than the Trapezoidal Rule even though at first glance it may appear the opposite of that. I also show how the error bound estimate sometimes are much larger than the actual error for any given approximation. This is a very important video as it goes in detail on the concept of integral approximation and especially accuracy, so make sure to watch this video!

Download the notes in my video:

Notes: https://1drv.ms/b/s!As32ynv0LoaIheVFwSO716HT3ufJOg
Excel File: https://1drv.ms/x/s!As32ynv0LoaIheRaio5vyKMD_mpbbg?e=fw7ehp

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/approximate-integration-accuracy-and-error-bounds

Related Videos:

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 .

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