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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.(a) Give upper and lower estimates for the total quantity $Q(6)$ of erupted materials alter six seconds.(b) Use the Midpoint Rule to estimate $Q(6)$.

## a)Upper estimate $=220$ tonnesLower estimate $=172$ tonnesb)200 tonnes

Integrals

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##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

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