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Changing the order of integration is worth doing chiefly when

  • A.the inner integral has no elementary antiderivative in the given order
  • B.the region of integration is a rectangle
  • C.the integrand is a product of two functions
  • D.the limits are all constants

Answer: A

The classic case is \( \int_{0}^{1}\!\int_{x}^{1} e^{-y^{2}}dy\,dx \), where the inner integral cannot be done in the order given but becomes elementary when reversed. With a rectangle and constant limits the order makes no difference to the difficulty, so there is nothing to be gained by swapping

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