Thanks Chris, that should help Juriemagic to understand the rectangle idea.
The rectangles can be represented in a number of different ways.
They are estimates of the area under the curve and in certain cases they can give exact areas.
I'd just like to talk a little more about this.
Jurimagic,
You know how the integral sign looks like a stylized S ?
Well that is not a coincidence.
That S stand for sum.
Consider definite integrals where there is a number at the bottom B and a number at the top T and it is dx
The integral will will give the sum of the areas of the rectangles that are under she curve between B and T.
The rectangles will be evenly spaced along the x axis between the lowest value B and the highest value T
The width of the rectangles is the difference between 2 adjacent x values. ie dx d stands for difference.
For example if two adjacent x values are 3 and 4 then the difference between them is 4-3=1 This is the width of the rectangle.
ONLY with integration the difference between the x values approaches 0
So a definite integral give the sum of an infinite number of infinitely thin rectangles and hence gives the accurate area under the curve.
I am not sure if you can understand what I am saying when I have not any diagram to show you.
Try drawing what i have described.
If you want me to try and explain better ask and I will try. :)