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

Discussion

True or false: the Jacobian factor in a change of variables may be negative.

  • A.True, provided the region is traversed clockwise
  • B.False, its modulus being taken because area is positive
  • C.True, the sign recording that the map reverses orientation
  • D.True, whenever the transformation is not linear

Answer: B

The determinant itself may well be negative, and its sign does record a reversal of orientation. But the area element uses its modulus, so the factor entering the integral is never negative; otherwise a positive integrand over a genuine region could return a negative total

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

Post your comment

Please log in or register to post a comment.