# Double Integral Sample Points

1. Jul 7, 2009

### bphysics

1. The problem statement, all variables and given/known data
I am getting rather confused when I attempt to solve one of these double integral problems.

A typical problem is phrased like this:
If R = [-1, 3][3,5], use a Riemann sum with m = 4, n = 2 to estimate the value of the following
$$\int\int(y^{2}-2x^{2}$$

The problem will then say something like "Take the sample points to be the upper left corners of the squares." What does this mean? There seems to be four seperate conditions -- upper left corners, lower left corners, upper right corners, lower right corners.

I am trying to understand what each of these conditions means and how it changes how I solve the problem (I believe it typically changes my x/y set to use).

2. Jul 7, 2009

### Office_Shredder

Staff Emeritus
If I understand correctly, you're drawing squares inside of the rectangle and estimating the integral by multiplying the area of each square by the value of the function at a point in the square, then adding all of these together. In this particular case it says to use the value of the function in the upper left corner of each square... you solve the problem in exactly the same way only you have slightly different values for your estimate of the function in each square you've drawn