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Suppose that a volcano is erupting and readings of the rate r(t) at which solid materials are spewed into the atmosphere are given in the table. The time t is measured in seconds and the units for r(t) are tonnes (metric tons) per second.
t 0 1 2 3 4 5 6 r(t) 2 12 26 32 48 56 60
(a) Give upper and lower estimates for the total quantity Q(6) of erupted materials after 6 seconds using 6 subintervals.
Q(6) = 1 tonnes (lower estimate)Q(6) = 2 tonnes (upper estimate)
(b) Use the Midpoint with three subintervals to estimate Q(6).
Q(6) = 3 tonnes
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