Discussion
Put these steps of finding a volume by triple integration in order. 1. Integrate in the innermost variable 2. Choose the coordinate system that makes the boundary a constant coordinate 3. Work outwards through the remaining two integrals 4. Write the three ranges, innermost first
Answer: C
The coordinate system is chosen first, because it decides whether the limits are constants or functions. The three ranges are then written from the inside out, and the integrals evaluated in that order, each result becoming the integrand of the next. Choosing coordinates after writing the limits means writing them twice
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