Machine-translated by Google. Questions are authored in English.
Top

Discussion

True or false: the limits of a double integral may be interchanged along with the differentials, leaving everything else alone.

  • A.True, the differentials carrying the limits with them
  • B.True, unless the region is unbounded
  • C.False, the new limits having to be read from a sketch of the region
  • D.True, provided the integrand is continuous on the region

Answer: C

Only for a rectangle with constant limits does the swap leave the numbers unchanged. In general the limits describe the region in one particular order, and reversing the order means re-describing the same region, which needs the sketch. Continuity guarantees the two orders give the same *value*, not the same limits

No comment is present. Be the first to comment.
Loading…

Post your comment

Please log in or register to post a comment.