Chapter 5.8, Problem 13ES

Let $f\left(x\right)=3x^2$

(a) Find the arithmetic average of the values $f\left(0.4\right),f\left(0.8\right),f\left(1.2\right),f\left(1.6\right),$ and f(2.0).

(b) Find the arithmetic average of the values $f\left(0.1\right),f\left(0.2\right),f\left(0.3\right),\dots ,f\left(2.0\right)$ .

(c) Find the average value of $f$ on $\left[0,2\right]$ .

(d) Explain why the answer to part (c) is less than the answers to parts (a) and (b).