๐ Simpsons Rule - Approximate Integration ๐
๐ Approximating Definite Integrals Using Simpsonโs Rule โ Step-by-Step Example ๐
In this video, I demonstrate how to use Simpsonโs Rule to approximate a definite integral. The process is similar to approximating with trapezoids, but here we use parabolic segments instead of rectangles. While the approximating formula changes slightly, itโs straightforward once you recognize the pattern, particularly the alternating coefficients of 4 and 2 for the "middle" terms.
๐ Whatโs covered:
A full, detailed example of using Simpsonโs Rule to approximate the integral of 1 / (1 + x^5) from 0 to 3.
Explanation of the formula and how Simpsonโs Rule improves accuracy by utilizing parabolas.
Discussion of the pattern of middle coefficients (4 and 2) and how they fit into the approximation formula.
๐ข In this example, we use n = 6 to demonstrate how the rule applies to this integral and explain how to compute the approximation step by step. Whether youโre learning numerical methods or preparing for calculus exams, this video provides a clear guide to mastering Simpsonโs Rule.
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Watch video ๐ Simpsons Rule - Approximate Integration ๐ online without registration, duration hours minute second in high quality. This video was added by user patrickJMT 24 March 2009, don't forget to share it with your friends and acquaintances, it has been viewed on our site 898,215 once and liked it 4.8 thousand people.