📚 Simpsons Rule - Approximate Integration 📚
📚 Approximating Definite Integrals Using Simpson’s Rule – Step-by-Step Example 📚
In this video, I demonstrate how to use Simpson’s 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, it’s straightforward once you recognize the pattern, particularly the alternating coefficients of 4 and 2 for the "middle" terms.
🚀 What’s covered:
A full, detailed example of using Simpson’s Rule to approximate the integral of 1 / (1 + x^5) from 0 to 3.
Explanation of the formula and how Simpson’s Rule improves accuracy by utilizing parabolas.
Discussion of the pattern of middle coefficients (4 and 2) and how they fit into the approximation formula.
🔢 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 you’re learning numerical methods or preparing for calculus exams, this video provides a clear guide to mastering Simpson’s Rule.
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