Final answer:
Fubini's theorem may not work when the function being integrated is not absolutely integrable or when the region of integration is not properly defined.
Step-by-step explanation:
Fubini's theorem is a result in calculus that allows for the interchange of the order of integration in a multiple integral. However, there are some cases where Fubini's theorem may not work for proper regions.
One instance is when the function being integrated is not absolutely integrable over the region of integration. This means that the integral of the absolute value of the function diverges, making it impossible to apply Fubini's theorem.
Another case is when the region of integration is not a proper region. A proper region is one that can be described by a finite number of intervals or regions. If the region of integration is not properly defined, Fubini's theorem cannot be used.