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Simpson's Rule formula

  1. Jul 30, 2014 #1

    Maylis

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    Gold Member

    Hello,

    I was wondering if the formula

    ## \int_{a}^{b} f(x) \, dx \approx \tfrac{b-a}{6}\left[f(a) + 4f\left(\tfrac{a+b}{2}\right)+f(b)\right]. ##

    for simpson's rule is for when the number of partitions approaches infinity?
     
  2. jcsd
  3. Jul 30, 2014 #2

    olivermsun

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    Science Advisor

    The symbol ##\approx## means it's approximately equal, so this is always true depending on your definition of "approximate." :wink:

    The integral above is for a single partition, so the error decrease as the partition gets small. For a definite integral over some fixed limits a, b, then yes, it means the error decreases as you split the fixed interval into more partitions.
     
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