1. ## Riemann Integration

Ok look, I know limit integration but can someone explain how Riemann integration is any different. Because I can't figure out the difference based on what I've been told. This isn't a specific problem to solve, I just want to know what it is. They seem the same to me. But what is this about seperating the limits into blocks. Why do you have to do that? Why don't you just use the normal limit integration? Is it when you don't know the equation of the curve? Also what do you do once you have the maximum and minimum? Do you just leave the area as a range? I am confused.

2. Originally Posted by LumusRedfoot
Ok look, I know limit integration but can someone explain how Riemann integration is any different. Because I can't figure out the difference based on what I've been told. This isn't a specific problem to solve, I just want to know what it is. They seem the same to me. But what is this about seperating the limits into blocks. Why do you have to do that? Why don't you just use the normal limit integration? Is it when you don't know the equation of the curve? Also what do you do once you have the maximum and minimum? Do you just leave the area as a range? I am confused.
Dear LumusRedfoot,

The Riemann integration is a definition of the integral of a function. Using this definition and the concepts of derivatives we can prove that integration and differentiation are reverse processes (which is done through the Fundamental theorem of calculus - Wikipedia, the free encyclopedia). Although you may not notice, when you compute a definite integral you use the Fundamental theorem of calculus. So the normal limit integration is something that we can use to compute a integral but does not say what is integration.

3. hi

so how would i tackle a riemann integration problem them. i have been given no sugestion as to how the question would be in an exam but i was just told 'learn riemann integration'. im not in the taught group in the course (i am underage and studying from home with notes). unfortunately i dont get all the lecture notes. but i was just told learn riemann integration and i am stumped as to what i will get in the exam.

ps the dog is very nice its cute i like dogs

4. I'm wondering what you mean by "limit integration". "Riemann integration" is just the kind of integration you learn in first year Calculus (to distinguish it from the more general "Stieljes integral" and "Lebesque integral").

5. Originally Posted by HallsofIvy
I'm wondering what you mean by "limit integration"
definite integral, between two limits

. "Riemann integration" is just the kind of integration you learn in first year Calculus (to distinguish it from the more general "Stieljes integral" and "Lebesque integral").
it is going into partitions. the only info i have is a pdf which talks about partitions but it is very vague. it is talking about things like not using calculus but working out the area from rectangles, to get an estimate. but i have no example questions like saying how close you need to make the estimate

6. Originally Posted by LumusRedfoot
definite integral, between two limit
I suppose by that you mean finding the anti-derivative and substituting the upper limit and lower limit then subtracting. Sadly that is the misconception that must students have coming away from basic calculus.
But that is wrong.
When Prof Hals tells you that the Riemann Integral is the basic calculus integral, he means the is one way to evaluate an integral and under certain conditions it will agree with what you are call limit integral.
There are many different approaches to integrals.
There are functions that are Lebesgue Integrable but not Riemann Integrable. There are functions that are Denjoy Integrable but not Lebesgue Integrable; etc.
This actually was a very active area of research in the second half of the twentieth century. For example, McShane found a definition he called The Unified Integral which is completely equivalent to Lebesgue but uses Riemann type sums.

7. anti-derivative is not the prefered term.

anyway

here is the question

let p donate the aritition of the close dinterval [0,1] into ten equal sub intervals. determine the riemann left sum for f(x)= x, x^2 and e^x.

8. Originally Posted by LumusRedfoot
let p donate the paritition of the close dinterval [0,1] into ten equal sub intervals. determine the riemann left sum for f(x)= x, x^2 and e^x.
The sum $\displaystyle \sum\limits_{k = 0}^9 {f\left( {\frac{k}{{10}}} \right)\left( {0.1} \right)}$ answers that question.