Chapter 14.2, Problem 47E

(a)

To determine

To calculate: The internet sites Facebook and MySpace experiencing a larger influx of new members from the start of July $2005$ to the start $2007$ and estimation of number of people joined that internet sites rather joined its competitor during that period where the rate at which new members joined Facebook and MySpace in the period $2005$ to the middle of $2008$ is modeled by $f\left(t\right)=12t^2-20t+10$ $\left(0\le t\le 3.5\right)$ millions member per year and $m\left(t\right)=10.5t^2+25t+18.5$ $\left(0\le t\le 3.5\right)$ millions member per year.

(b)

To determine

The meaning of integral ${\displaystyle \underset{0.5}{\overset{2}{\int }}\left[m\left(t\right)-f\left(t\right)dt\right]}$, if Facebook and MySpace in the period $2005$ to the middle of $2008$ is modeled by $f\left(t\right)=12t^2-20t+10$ $\left(0\le t\le 3.5\right)$ millions member per year and $m\left(t\right)=10.5t^2+25t+18.5$ $\left(0\le t\le 3.5\right)$ millions member per year