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. (Assume that the rate $r(t)$ is always positive.) The time $t$ is measured in seconds, and the units for $r(t)$ are tonnes (metric tons) per second. $$\begin{array}{|c|c|c|c|c|c|c|c|}\hline {\it t} & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline {\it r} ({\it t}) & 2 & 10 & 24 & 36 & 46 & 54 & 60 \\ \hline \end{array}$$

(a) Give lower and upper estimates for the quantity $Q(6)$ of erupted materials after 6 seconds.

Lower estimate: tonnes

Upper estimate: tonnes

(b) Use the Midpoint Rule to estimate $Q(6)$. Midpoint Rule estimate: tonnes