1. Jan 17, 2010

### LucasGB

An integral can be defined as the limit (as n approaches infinity) of the sum of f(x)times Delta x. It has been said that f(x) can be taken at any point of the Delta x interval (at the right side, at the left side, at the center, etc.). My question is: can I pick f(x) at one point of the Delta x interval (let's say, the left) in one rectangle, and then in the next rectangle pick it in another point (let's say, the center), and so on, or once I make my choice of where I will choose the point, I must be consistent?

2. Jan 17, 2010

### hkBattousai

Yes, you can take it at any point inside the rectangle side. It doesn't change anything since dx apreaches to zero, so every where on the rectangle side aproaches to the same f(.) value. It will not change the value of the integral. But in applied mathmatics, if you use a computer software or a microcontroller (DSP chip, etc) to calculate the inegral, it will change the result very very very little for sufficiently enough dx values assuming that function is not changing too fast (i.e.; it doesn't have discontinuities). The error will be neglegible.

3. Jan 17, 2010

### LucasGB

Yes, I understand I can take it at any point inside the rectangle side, but can I pick it at different points in each rectangle? For example, I take it at the center in the first, at the left in the second, at the right in the third, etc. I'm inclined to think this is true, because as you said "it doesn't change anything since dx apreaches to zero, so every where on the rectangle side aproaches to the same f(.) value."

4. Jan 17, 2010

### hkBattousai

Yes you can take it at different points for each rectangle.

5. Jan 17, 2010