# How to find average rate of change How would I find the average rate of change over 8 minutes, of a person that runs at a rate of upsilon(t)=xsin(x^2−7x) ft/min? I missed when this was taught and I have no clue on how to do it. Help is greatly appreciated.

How to find average rate of change
How would I find the average rate of change over 8 minutes, of a person that runs at a rate of $v\left(t\right)=x\mathrm{sin}\left({x}^{2}-7x\right)$ ft/min? I missed when this was taught and I have no clue on how to do it. Help is greatly appreciated.
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Maffei2el
The average rate of change of a function f(t) over the interval [a,b] is $\frac{f\left(b\right)-f\left(a\right)}{b-a}$
The numerator f(b)−f(a) is the change in f, and b−a measures how long it took.
In this problem, you have to calculate the change in displacement. That will require integration.
To integrate, we would need to know the interval, which has not been specified. We know "b−a" but do not know b or a. Perhaps we are expected to assume that a=0 and b=8, but probably the problem as originally stated did not leave any ambiguity.