Approximate Integration: Example 6: Simpson's Rule Error

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.

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