Let $I=\int_{0}^{\,4} {f(x)}\, dx,$ where $f$ is the function whose graph is shown below.

(a) Use the graph to find $L_2,$ $R_2,$ and $M_2.$

$L_2 =$

$R_2 =$

$M_2 =$

(b) Are these underestimates or underestimates $I$?

? Underestimate Overestimate  1. $M_2$

? Underestimate Overestimate  2. $L_2$

? Underestimate Overestimate  3. $R_2$

(c) Use the graph to find $T_2.$

$T_2 =$

(d) Is $T_2$ an overestimate or underestimate of $I$?

? Underestimate Overestimate  1. $T_2$

(e) For any value of $n$, list the numbers $L_n,$ $R_n,$ $M_n,$ $T_n,$ and $I$ in increasing order. For each of the five values, order them from 1 to 5, with 1 indicating the smallest of the five values and 5 being the largest of the values.

? 1 2 3 4 5  1. $T_n$

? 1 2 3 4 5  2. $L_n$

? 1 2 3 4 5  3. $M_n$

? 1 2 3 4 5  4. $R_n$

? 1 2 3 4 5  5. $I$