61.15 Simpson and the circle

Extract

A favourite exercise on Simpson’s rule is to evaluate π as the area of a quadrant of a circle of radius 2, i.e. as the area under y = √(4 – x²) from x = 0 to x = 2. It is somewhat discouraging, and a poor advertisement for the technique, to arrive at the answer 3·127 008 with intervals of width 0·2.