Calculating Even N with Simpson's Rule

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Simpson's Rule requires an even number of intervals to accurately approximate curves using parabolas. Each parabola in the rule is defined by three points, necessitating that the total number of points used be odd. For example, using one parabola divides the interval into two sub-intervals, while two parabolas create four sub-intervals by sharing a point. This structure ensures that the method can effectively capture the behavior of the function being integrated. Understanding this requirement is crucial for correctly applying Simpson's Rule in calculus.
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why do we use n as even number with simpson's rule ?

 
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Thread moved to calculus homework. pari786 -- tell us what you know about Simpson's rule.
 
Simpson's rule approximates the curve by a series of parabolas each of which requires 3 points. Using one parabola would mean 3 points dividing the entire interval into 2 sub-intervals. Using 2 parabolas would mean 5 points they share one point), so 4 sub-intervals, etc.
 

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