Worksheet 6.1 - Integral As Net Change - Calculus Maximus Page 2
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9Calculus Maximus
WS 6.1: Integral as Net Change
3. The rate at which customers arrive at a counter to be served is modeled by the function F defined by
t
t
F t
12 6cos
for
0, 60
, where
F t is measured in customers per minute and t is
measured in minutes. To the nearest whole number, how many customers arrive at the counter over the
60-minute period?
(A) 720
(B) 725
(C) 732
(D) 744
(E) 756
0.5
t
4. Pollution is being removed from a lake at a rate modeled by the function
y
20
e
tons/yr, where t is
the number of years since 1995. Estimate the amount of pollution removed from the lake between 1995
and 2005. Round your answer to the nearest ton.
(A) 40
(B) 47
(C) 56
(D) 61
(E) 71
0.2
t
5. A developing country consumes oil at a rate given by
r t
20
e
million barrels per year, where t is
time measured in years, for 0
. Which of the following expressions gives the amount of oil
t
10
consumed by the country during the time interval 0
t
10
?
10
10
r
(A)
r
10
(B)
r
10
r
0
(C)
r t dt
(D)
r t dt
(E)
10
10
0
0
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