Discussion
Consider the following statements about changes of variable. 1. The Jacobian factor is the modulus of a determinant 2. A change of variables can turn a hard region into a simple one 3. The Jacobian may be omitted when the transformation is linear
Answer: B
The first two hold, and simplifying the region is often the whole reason for the change. The third is false: a linear map has a *constant* Jacobian, which is easy to compute but is not one unless the map preserves area. Scaling by two in each direction multiplies areas by four, and that factor must appear
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