Simpsons's Rule Integration

Simpson's Rule uses parabolas to approximate the curve, represented in the above diagram by parabolas
f1--f2--f3 and f3--f4--f5. Simpson's Rule can be expressed as:

(f1/3 + 4f2/3 + 2f3/3 + 4f4/3 + ... + 2fN-2/3 + 4fN-1/3 + fN/3)*dx

Simpson's Rule requires an even number of intervals (steps).

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