Discussion
Consider the following statements about multiple integrals. 1. The polar area element carries a factor of \( r \) 2. The order of integration may always be exchanged without changing the limits 3. A triple integral with integrand one gives a volume
Answer: C
The first and third are standard. The second is false in general: the limits describe the same region read a different way, and only for a rectangle with constant limits do they survive the exchange unchanged. For a triangle or a region under a curve they must be recomputed from the sketch
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