Topic: Riemann Integral
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What is Riemann integral?
( ′rē′män ′int·ə·grəl ) (mathematics) The Riemann integral of a real function ƒ(x) on an interval (a,b) is the unique limit (when it exists) of the sum of ƒ(ai)(xi - xi-1), i = 1, …, n, taken over all partitions of (a,b), a = x0 <a1 <x1 < &cellip;... Read More »
Source: http://www.answers.com/topic/riemann-integral
What is the difference between Riemann and Lebesgue integral?
The Lebesgue integral covers a wider variety of cases. Specifically, the definition of hte Riemann integral permits a finite number of discontinuities; the Lebesgue integral permits a countable infinity of discontinuities. Read More »
Source: http://wiki.answers.com/Q/What_is_the_difference_between_Riemann_...
What is Riemann Integration like?
A Riemann sum gives you an estimate which is either too high (if you use right endpoint) or too low (if you use the left endpoint). Try finding an example using a search engine like Google. Good luck to you ! Read More »
Source: http://answers.yahoo.com/question/index?qid=20080813072809AA4lVBN
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Riemann Integral
(n.) The numerical measure of the area bounded above by the graph of a given function, below by the x-axis, and on the sides by ordinates drawn at the endpoints of a specified interval; the limit, as the norm of partitions of the given interval approach
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Answers to Other Common Questions
Integral of a function f on a set X exists and is ...
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Source: http://www.chacha.com/question/how-is-a-lebesgue-integral-differe...
First, it helps to know that the integral is expected to be zero, and for any partition P the lower sum L(f,P) = 0, by the way f is defined. So it suffices to show that for any ε > 0, you can find a partition P such that the upper sum U(f, ...
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Source: http://answers.yahoo.com/question/index?qid=20110118090029AAg33iZ
The relationship between a definite integral and a riemann sum is that they both find the exact area under the curve. A riemann sum, as you probably know, is just adding up all the rectangles (infinity rectangles) under a curve. When you ma...
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Source: http://answers.yahoo.com/question/index?qid=20070302094941AAU2vAB
I thought they teach this in Indian kindergardens ... If you have a function y=f(x), Riemann integral takes a bunch of x's, gets corresponding y's, and adds them up. Measure integral takes a bunch of y's, looks at what x's result in f being...
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Source: http://answers.yahoo.com/question/index?qid=1006050431937
Back in the 60's when I took calc, we usually thought of a Riemann sum ("RS") as being an over or under approximation only for monotone functions. Because f(x) is piecewise monotone, you'd probably say that the RS is an over approximation o...
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Source: http://answers.yahoo.com/question/index?qid=20100103183420AAbIfrm
Given a function f(x) for x in [a,b], a Riemann sum over this interval is a partitioning of the interval into n subintervals with the boundaries: a = x0 < x_1 < x_2 < ... < x_n = b ("_" indicates a subscript), to form the sum: S_n = Σ (x_i ...
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Source: http://answers.yahoo.com/question/index?qid=20100109135148AAeR4WB
