Use a ﬁnite sum to estimate the average value of the function on the given interval by partitioning the interval and
evaluating the function at the midpoints of the subintervals.
-$f ( x ) = 8 | x |$ on $[ - 3,3 ]$ divided into 4 subintervals
A) 48
B) 12
C) $\frac { 16 } { 3 }$
D) 18

Question

Quizplus · Accepted Answer

The interval $[-3,3]$ is divided into 4 subintervals: $[-3,-1.5]$, $[-1.5,0]$, $[0,1.5]$, and $[1.5,3]$. The midpoints of these intervals are $-2.25$, $-0.75$, $0.75$, and $2.25$, respectively. Evaluating the function $f(x) = 8|x|$ at these midpoints gives $18$, $6$, $6$, and $18$, respectively. The average value is then $\frac{1}{4}(18 + 6 + 6 + 18) = 12$.

Use a ﬁNite Sum to Estimate the Average Value of the Function