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A reduction formula for an integral is useful because it

  • A.evaluates the integral in closed form at a single step
  • B.converts the integral into a derivative of the integrand
  • C.replaces the integral by a numerical estimate
  • D.expresses the integral in terms of the same integral of lower index

Answer: D

A reduction formula such as \( I_{n} = \tfrac{n-1}{n} I_{n-2} \) steps the index down until a base case is reached, so a whole family is handled by one relation plus one or two starting values. It is a recursion, not a closed form, and nothing about it is numerical or a differentiation

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