Chapter 4.3, Problem 69E

The rate of memorizing information initially increases. Eventually, however, a maximum rate is reached, after which it begins to decreases.

Suppose an experiment finds that rate the rate of memorizing is given by

$M^{\prime }\left(t\right)=-0.009t^2+0.2t,$

Where $M^{\prime }\left(t\right)$ is the memory rate, in words per minute. How many words are memorized in the first 10 min $\left(\text{from }t=0\text{ to }t=10\right)$?