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Integration by parts is the integral counterpart of

  • A.the product rule for derivatives
  • B.the chain rule for derivatives
  • C.the quotient rule for derivatives
  • D.the mean value theorem

Answer: A

Integrating \( (uv)' = u'v + uv' \) and rearranging gives \( \int u\,dv = uv - \int v\,du \). So the method undoes a product rule. The chain rule's counterpart is substitution, and the quotient rule has no integral method of its own, quotients being handled by partial fractions or substitution instead

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