Discussion
Match the numerical rule with the degree of polynomial it integrates exactly. 1. Trapezoidal 2. Simpson's one-third 3. Simpson's three-eighths P. Cubic, using four ordinates Q. Linear, using two ordinates R. Cubic, using three ordinates
Answer: B
The trapezoidal rule joins two ordinates by a chord and is exact for a straight line. Simpson's one-third fits a parabola through three ordinates but is exact up to a cubic, the cubic error terms cancelling. The three-eighths rule uses four ordinates and a cubic fit, so it too is exact to that degree
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