Which of the following samples would meet the "random" condition?
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Using the shell method, the volume is given exactly by the definite integral,
Splitting up the interval [0, 1] into 5 subintervals gives the partition,
[0, 1/5], [1/5, 2/5], [2/5, 3/5], [3/5, 4/5], [4/5, 5]
with left and right endpoints, respectively, for the -th subinterval
where . The midpoint of each subinterval is
Then the Riemann sum approximating the integral above is
(compare to the actual value of the integral of about 14.45)