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True or false: Simpson's one-third rule is exact for a cubic integrand.

  • A.False, the rule being exact only for a linear integrand
  • B.True, but only when the number of strips is a multiple of three
  • C.True, the cubic error terms cancelling between the strips
  • D.False, the rule fitting a parabola and so exact only to degree two

Answer: C

Although the rule interpolates with a parabola, its error term involves the fourth derivative, which vanishes for a cubic. So the rule integrates cubics exactly, gaining a degree over what the fitting polynomial suggests. The multiple-of-three condition belongs to the three-eighths rule

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