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'right hand rule'
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| Title of object: |
right hand rule |
| Canonical Name: |
RightHandRule |
| Type: |
Definition |
| Created on: |
2006-06-08 16:27:23 |
| Modified on: |
2006-06-08 16:44:08 |
| Classification: |
msc:26A42, msc:41-01 |
Preamble:
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\usepackage{amssymb}
\usepackage{amsmath}
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%\usepackage{psfrag}
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Content:
The {\sl right hand rule\/} for computing the Riemann integral $\int_a^b f(x) \, dx$ is
$$\int_a^b f(x) \, dx = \lim_{n \to \infty} \sum_{j=1}^n f \left( a + \frac{(b-a)j}{n} \right) \left( \frac{b-a}{n} \right).$$
The Riemann integral can be approximated by using a definite value for $n$ rather than taking a limit.
If the Riemann integral is considered as a measure of area under a curve, then the expressions $f \left( a + \frac{(b-a)j}{n} \right)$ represent the heights of the rectangles, and $\frac{b-a}{n}$ is the common width of the rectangles. |
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