§4.2 Riemann sums (continued)

Summary

For $f(x) = 3x + 4$ on $[2, 5]$ with four subintervals, the midpoint sum $M_4$ equals

The sum $S = ((1.4)^2 + 1)0.4 + ((1.8)^2 + 1)0.4 + \cdots + ((3.0)^2 + 1)0.4$ is a right Riemann sum for which function and interval?

A braking car has velocity readings every $0.3$ seconds from $t = 0$ to $t = 1.8$. The midpoint estimate $M_3$ for stopping distance equals

A pollution escape rate $r$ increases over four weeks. With midpoint samples $0.6, 1.1, 1.8, 2.9$ tons per week and weekly panels, $M_4$ and a safe upper bound within one ton are

For the same braking data, compute the left endpoint estimate $L_6$ of the stopping distance in feet.

For the same braking data, compute the right endpoint estimate $R_6$ of the stopping distance in feet.

With $r(t) = 0.5e^{0.5t}$ on $[0,4]$ and five subintervals of width $0.8$, the left sum evaluates to approximately what value? Round to three decimals.

For a linear function, the midpoint sum $M_n$ equals the exact area under the graph for every positive integer $n$.