3/14/24, 7:06 PM
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Using Simpson's 1/3 rule with the given number of segments, I computed the integral over the defined range.
Final Answer
The numerical integration of the given function using Simpson's 1/3 rule with 16 segments is approximately .
Key Concept
Numerical Integration using Simpson's 1/3 Rule
Key Concept Explanation
Simpson's 1/3 rule is a numerical method for estimating the integral of a function. It works by approximating the region under the graph of the function with a series of parabolas that pass through multiple points on the graph. The rule requires an even number of equally-spaced intervals (or segments) and uses a weighted average to obtain the final approximation. The more segments used, the better the approximation becomes, assuming the function behaves nicely in the interval of integration.
Related Knowledge or Questions
[1] How does the accuracy of Simpson's 1/3 rule compare to the trapezoidal rule for the same number of segments?
[2] What would be the impact on the result if we doubled the number of segments in Simpson's rule?
[3] Can you solve the same integral using Simpson's 3/8 rule, and compare it with the Simpson's 1/3 rule result?
Keep up the good work, and don't hesitate to choose one of the related knowledge points or ask another question to deepen your understanding! 8.571415
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