Simpson's Rule Formula: Number of Partitions ∞

[gfd43tg]

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?

 

[olivermsun]

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

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.