Question

The position of an object is given by
p(t)=3t^2-2t+9
what is the average velocity of the object from t=-1 to 5=1?

Answer 1

The average of a function f(x) over an interval [a,b] is,\[\frac{1}{b-a}\int\limits_{a}^{b}f(x) dx\]Here, \[\frac{1}{1-(-1)}\int\limits_{-1}^{1}3t^2-2t+9dt \rightarrow \frac{1}{2}[t^3-t^2+9t]_{-1}^1\]\[=\frac{1}{2}(9-(-11))=10\]