Which are perfect cubes?
2 answers:
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Split up the interval [2, 5] into 
equally spaced subintervals, then consider the value of 
at the right endpoint of each subinterval.
The length of the interval is
, so the length of each subinterval would be 
. This means the first rectangle's height would be taken to be 
when 
, so that the height is 
, and its base would have length 
. So the area under over the first subinterval is 
.
Continuing in this fashion, the area under over the 
th subinterval is approximated by 
, and so the Riemann approximation to the definite integral is
and its value is given exactly by taking
. So the answer is D (and the value of the integral is exactly 39).
The length of the interval is
Continuing in this fashion, the area under
and its value is given exactly by taking