\frametitle{Average Value of a Function}
  If we let $n$ go to infinity:
    \lim_{n \to \infty} \frac{1}{b-a}\sum_{i = 1}^n f(x_i)\Delta x
  we get\pause
    \frac{1}{b-a} \int_a^b f(x) \, dx
  As a consequence, we have
    The average value $f_{\text{avg}}$of a function $f$ on an interval $[a,b]$ is:
      f_{\text{avg}} = \frac{1}{b-a} \int_a^b f(x) \, dx
    Thus the average value of the function is the integral over the interval divided by the width of the interval.