Answer
a. $64$
b. $236$
c. $136$
Work Step by Step
Subdividing $[0,6]$ (length 6) into three intervals, each has length 2.
$\begin{array}{llll}
int. & left & mid. & right\\
[0,2] & f(0)=-6 & f(1)=0 & f(2)=8\\
[2,4] & f(2)=8 & f(3)=18 & f(4)=30\\
[4,6] & f(4)=30 & f(5)=50 & f(6)=80
\end{array}$
a. Left endpoint estimate$:$
$[-6+8+30](2)=64$
b. Right endpoint estimate$:$
$[8+30+80 ](2)=236$
c. Midpoint estimate:
$[0+18+50 ](2)=136$
If $f$ is increasing, then
(a) is below the actual value and
(b) is above the actual value .
(c) is the closest to the actual value
