There is an assumption here that left and right is well understood in a multidimensional scenario.
Since I was raised in the USA I think of number lines being arranged with lesser numbers on the left. It is possible that people from other cultures may have other legitimate ways of arranging things. You will have to know which way your mathematical community does things.
Definition is everything in Math.
I will assume that m is the number of sub-divisions of the x direction and that n is the number of sub-divisions of the y direction. It is my understanding that some instructors use "m & n" to denote the number of points inserted to create sub-divisions and therefore an extra region would be created in both directions. You will need to clear that with your instructor. …show more content…
The area of each square is therefore 2*2=4 and the volume of each column will be 4 times the height of the right-right corner.
The 6 points are therefore
(4,2) xy=8 volume=32
(4,4) xy=16 volume=64
(6,2) xy=12 volume=48
(6,4) xy=24 volume=96
(8,2) xy=16 volume=64
(8,4) xy=32 volume=128
The sum of these numbers is height of a stack of columns would be 108
The sum of the volumes is 432
To check the arithmetic I also multiply 108 time 4 to get 432.
Since this is a monotonically increasing situation this estimate will be greater than the actual volume.

I will assume that the midpoint rule will also use the same number of sub-divisions.
The points are therefore as follows x is from the set{3,5,7} and y is from the set{1.3}
(3,1) xy = 3 volume=12
(3,3) xy = 9 volume=36
(5,1) xy = 5