Discussion
Put these steps of finding a volume of revolution in order. 1. Square the radius and multiply by \( \pi \) 2. Integrate between the limits 3. Identify the axis and the radius of a typical slice 4. Sketch the region and fix the limits of integration
Answer: D
The sketch settles which variable runs and between what values, so it comes first. The axis then determines what counts as the radius of a slice, which is squared and scaled to give the slice volume. Integration is the last step, and attempting it before the radius is identified is what produces the wrong power of \( y \)
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