Hi CPhill,
thank you for replying, but that is not it....the line they draw is actually a very narrow rectangular, and it stretches from the x axis upwards to where it meets the graph. I know it is not anything to do with symmetry since it is plotted anywhere (of course calculated).
the book explains how in the past before Integration was developed, small rectangles were used to get an approximate area size. So the area would be filled with rectangles as narrow as possible (x values), and then were the areas of each rectangle calculated and then added together. The area of each rectangle is lb, so since the rectangles are positioned vertically, the length would be y and the breadth would be \(\Delta x\). The greater this value, the less accurate the final answer. (Total Area)
Then they explain that integration makes the \(\Delta x\) value to be zero, thus we have millions of very thin rectangles (with lengths (y) and zero breadths) of which the areas need to be calculated and added together, hence the introduction to integration. Now, one of these "strips" are called "a representative strip"....please bear in mind I translated directly from Afrikaans...so this may not even be the true name for it.
The question is: Show the "representative strip" you are going to use to calculate the area. Then the second question is to use integration to actually calculate the area size.
If nothing makes sense, I will understand....Thanx for trying though...
...