009B Sample Midterm 3, Problem 4

The rate of reaction to a drug is given by:

$r'(t)=2t^{2}e^{-t}$

where $t$ is the number of hours since the drug was administered.

Find the total reaction to the drug from $t=1$ to $t=6.$

Foundations:
If we calculate $\int _{a}^{b}r'(t)~dt,$ what are we calculating?
We are calculating $r(b)-r(a).$ This is the total reaction to the
drug from $t=a$ to $t=b.$

Solution:

Step 1:

Step 2:

Step 3:

Final Answer:

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