Use a Riemann sum with m $=3,$ n $=2,$ and take the sample point to be the upper right corner of each square.

Step $1$

We are requested to use m $=3$ and n $=2$ over the rectangle

R $=$

$($x$,$ y$)|3$ x $9,7$ y $11$

The subrectangles are, therefore, as follows.

We can estimate the volume of the given solid using the Riemann sum

$3$i $=1$

$2$f$($xi$,$ yj$)$Aj $=1$

$,$

with

f$($x$,$ y$)=$ xy$.$

Since $3$ x $9$ and m $=3,$ then $$x $=2$

$2$

$,$ and since $7$ y $11$ and n $=2,$ then $$y $=2$

$2$

$.$ Consequently, we have

$$A $=4$

$4$

$.$

Step $2$

When i $=1$ and j $=1,$ we are referring to the coordinates of the rectangle in the lower left corner of the grid. We are told to use the upper right corner as a sample point. Therefore, for i $=1$ and j $=1,$ the sample point would be

$($x$,$ y$)=$

$7,5$

$.$