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# Simplifying Integration Question watch

1. Hey.

Using I to stand for the integral sign:

I s dx + I t dx = I (s+t) dx (where s and t are functions of x).

Why is the above statement true?
2. What level are you working at? If it's A-level then just accept the answer "it just is"; if it's not, then you need to consider the definition of Riemann integrability. If and denote the lower and upper sums of on a partition respectively, then note that:

3. (Original post by nuodai)
What level are you working at? If it's A-level then just accept the answer "it just is"; if it's not, then you need to consider the definition of Riemann integrability. If and denote the lower and upper sums of on a partition respectively, then note that:

A Level. It has come up in a STEP question. Working the othet way then I would say that would be acceptable, i.e. I (s+t) dx = I s dx + I t dx, because that is what I do when integrating. Integrate each term seperately just like I would do for differentiation. I suppose that tells me that the two must be equal but I was looking for a better explaination. However, it looks as though the proper explaination is too complex for me! haha
4. At A-level, you should just assume that (for any real numbers ).

Edit: Well, actually at *any* level, unless you're specifically asked to prove it.

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