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Approximate Integration: Example 6: Simpson's Rule Error

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First published at 21:42 UTC on August 8th, 2019.

#mathematics
#calculus
#science

Math Easy Solutions

MES

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In this video I go over a very useful example on applying the Simpson's Rule error bound formula to determine the adequate number of sub-intervals needed to ensure a given accuracy, in this case being within 0.0001. The integral being approximated is the same the integral of the function 1/x from x = 1 to x = 2. This is the same function as in example 2 which was approximated using the Trapezoidal and Midpoint Rules. This video shows how the Simpson's Rule can achieve the same accuracy at a far less number of sub-intervals. This means that a calculator or computer program would need less calculations and thus less computing power to achieve a high level of accuracy. In very advanced mathematical and physics applications, such as fluid dynamics, and airplane modelling, lowering the required computing power is of utmost importance. I go over briefly about computing and mathematical approximation in this video and it would be pretty interesting for you watch this video and learn from.

Download the notes in my video: http://1drv.ms/1KJl091

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/approximate-integration-example-6-simpson-s-rule-error

Related Videos:

Simpson's Rule Approimation: Error Bound Proof: https://youtu.be/q8jD7U0_BSs
Relating Simpson's Rule with Trapezoidal and Midpoint Rules: https://youtu.be/lX2UYAm7A90
Approximate Integration: Example 4: Simpson's Rule: https://youtu.be/7xpdZnT6IWU
Approximate Integration: Simpson's Rule: Proof: https://youtu.be/aDvSpOHQoLU
Approximate Integration: Midpoint Rule Error Bound: Proof: http://youtu.be/aKUFHXNeW7Y
Approximate Integration: Example 2: Accuracy: http://youtu.be/D9l2o-UiRLE
Approximate Integration: Accuracy and Error Bounds: http://youtu.be/WTdNktL_1Uc
Approximate Integration: Trapezoidal Rule Error Bound: Proof: http://youtu.be/_mrSHIin7Mw
Integration by Parts: Integration Constants: http://youtu.be/jJ-RJTNMy4s
Evaluating Integrals - Midpoint vs Right Endpoint Approximations Comparison: http://youtu.be/3x3sF7P9xfY
Derivative of y = x^n - Part 2: General Power Rule: http://youtu.be/Ibvu33oh49o .