Definition:Element of Integration
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Definition
Consider the indefinite integral:
- $\ds \int \map f x \rd x$
or the definite integral:
- $\ds \int_a^b \map f x \rd x$
The part of the expression after the integral sign:
- $\map f x \rd x$
is known as the element of the integration operation.
Examples
Element of Area
Consider the definite integral:
- $\ds \int_a^b \map f x \rd x$
This gives the area under the curve whose locus is given by $y = \map f x$
Hence the element of integration $\map f x \rd x$ can be interpreted as an infinitesimal strip of area.
These are then summed to find the total area under the curve.
Also see
- Results about elements of integration can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): element: 1.
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): element: 1.