Definition:Riemann Sum
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Definition
Let $f$ be a real function defined on the closed interval $\mathbb I = \left[{a..b}\right]$.
Let $\Delta$ be a subdivision of $\mathbb I$.
For $1 \le i \le n$, let $\Delta x_i = x_i - x_{i-1}$, and let $c_i \in \left[{x_{i-1} .. x_i}\right]$.
The sum:
- $\displaystyle \sum_{i=1}^n \ f\left({c_i}\right) \ \Delta x_i$
is called a Riemann Sum of $f$ for the subdivision $\Delta$.
Geometric Interpretation
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Also see
Source of Name
This entry was named for Georg Friedrich Bernhard Riemann.
Sources
- Roland E. Larson, Robert P. Hostetler and Bruce H. Edwards: Calculus: 8th Edition (2005): $\S 4.3$
- Weisstein, Eric W. "Riemann Sum." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/RiemannSum.html
