Definition:Element of Integration

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.