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Approximate Integration: Example 7: Simpson's Rule Accuracy

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First published at 04:24 UTC on June 19th, 2019.

#mathematics
#calculus
#science

Math Easy Solutions

MES

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In this video I go over another example on approximate integration and this time use the Simpson's Rule to approximate the integral from x = 0 to x = 1 of the function e^(x^2). This particular function has no definite integral formula so approximating it is the only way of calculating its integral. In this video I show that the accuracy using the Simpson's Rule is an order of magnitude better than using the Midpoint Rule to approximate this same integral, as shown in example 2 of this video series.

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

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/approximate-integration-example-7-simpson-s-rule-accuracy

Related Videos:

Approximate Integration: Example 6: Simpson's Rule Error: https://youtu.be/jgrdYT-9IGY
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 .