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Approximate Integration: Left, Right, Midpoint, and Trapezoidal Rules

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First published at 06:48 UTC on August 1st, 2019.

#mathematics
#calculus
#science

Math Easy Solutions

MES

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In this video I go over the topic of approximate integration and explain how for the situations which the antiderivative can't be found or for experimental data where there is no formula, making an approximation of a definite integral is the only way to go. I go over 4 types of Riemann Sums Approximation methods: Left Endpoint, Right Endpoint, Midpoint and Trapezoidal Approximations methods. I went over Riemann Sums in my earlier video on definite integrals and showed that Riemann Sums are simply approximations of integrals using rectangles but when summed up to infinite they form the exact integral. In this video though, I focus on the 4 already mentioned approximation types and preview the fact that the Midpoint Rule is the most accurate approximation even though the Trapezoidal Rule appears at first glance as the most accurate. I explain this in detail in later videos so stay tuned!

Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!94835&authkey=!ALofG7kJIusyjGM&ithint=file%2cpdf

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/approximate-integration-left-right-midpoint-and-trapezoidal-rules

Related Videos:

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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