For Problems $16$ thru $19,$ find the volume of the solid obtained by revolving the region as described below. See Figure $9\mathrm{.}6-2.$

$16.R_1$ about the $x-$axis.

$17.R_2$ about the $y-$axis.

$18.R_1$ about the line $B{C}^{\text{h}\text{a}\text{r}\text{r}}.$

$19.R_2$ about the line $A{B}^{\text{h}\text{a}\text{r}\text{r}}.$

$20.$ The function $f(x)$ is continuous on $0,12$ and the selected values of $f(x)$ are shown below.

Figure $9\mathrm{.}6-2$

$\backslash$table$[[x,0,2,4,6,8,10,12],[f(x),1,2\mathrm{.}24,3,3\mathrm{.}61,4\mathrm{.}12,4\mathrm{.}58,5]]$

Find the approximate area under the curve of $f$ from $0$ to $12$ using three midpoint rectangles.