Comparing Volumes of Revolution
Consider the region under from x = a to 9. Rotating this region about the x-axis yields a volume given by
(for a proper antiderivative, note that here the effective volume is proportional to , and using the given data, assume the computed volumes for a = 1, 2, 3, and 4 are approximately 40π, 38.5π, 36π, and 32.5π respectively). Rank the intervals [0,1], [0,2], [0,3], [0,4] in order of increasing volume when the lower limit a is varied (interpret [0,a] as indicating the region starting at x=a to x=9).
A
[4,9], [3,9], [2,9], [1,9]
B
[4,9], [2,9], [3,9], [1,9]
C
[3,9], [4,9], [2,9], [1,9]
D
[1,9], [2,9], [3,9], [4,9]
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