The average value of the function f(x) = (x-1)^2 on the interval from x=1 to x=5 is:
a) -16/3
b) 16/3
c) 64/3
d) 66/3
e) 256/3
why did they divide by 4? and how do they know what to integrate?
Definition: Let $\displaystyle f(x)$ be an integrable function on the closed interval $\displaystyle [a,b]$. Then the average value of $\displaystyle f(x)$ on $\displaystyle [a,b]$ is given by:
$\displaystyle \mbox{Average Value} = \frac 1{b - a} \int_a^b f(x)~dx$