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Interchanging the limits of a definite integral

  • A.reverses its sign
  • B.leaves it unchanged
  • C.makes it the reciprocal
  • D.makes it the absolute value of itself

Answer: A

By definition \( \int_{b}^{a} f = -\int_{a}^{b} f \), which is what makes the additivity rule \( \int_{a}^{b} + \int_{b}^{c} = \int_{a}^{c} \) hold for any arrangement of the three points. The convention is not a separate rule but a consequence of writing the increment of the antiderivative as \( F(b) - F(a) \)

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