To approximate the volume with 8 boxes, we have to split up the interval of integration for each variable into 2 subintervals, [0, 1] and [1, 2]. Each box will have midpoint 
that is one of all the possible 3-tuples with coordinates either 1/2 or 3/2. That is, we're sampling 
at the 8 points,
(1/2, 1/2, 1/2)
(1/2, 1/2, 3/2)
(1/2, 3/2, 1/2)
(3/2, 1/2, 1/2)
(1/2, 3/2, 3/2)
(3/2, 1/2, 3/2)
(3/2, 3/2, 1/2)
(3/2, 3/2, 3/2)
which are captured by the sequence
with each of 
being either 1 or 2.
Then the integral of 
over 
is approximated by the Riemann sum,
(compare to the actual value of about 4.159)
Always negative when dealing with expontents
The domain of a function is the set of values that can be used for x.
Here, x represents the number of tacos.
He can order no taco, so x = 0.
He can order 1 taco, where x = 1.
He can order 2 tacos, so x = 2.
He cannot order a fraction of a taco, so x cannot be a mixed numeral.
He can order as many tacos as he wants, so x can be any whole number, 0 to infinity.
The domain is all whole numbers.
You would have to calculate the percent first.
Add the total number of students
3420+4680= 8100 students TOTAL
Then you would divide the amount of students by the total
3420 part time/8100 students total = .42 or 42%
4680 full time/8100 total = .58 or 58%
Then you multiply the percentages by 90
(90)(.58)= 52.2
(90)(.42)= 37.8
Rounded
52 full time and 38 part time students
