Difference between revisions of "Integral"

Revision as of 21:03, 15 November 2007

The integral is a generalization of area. The integral of a function is defined as the area between it and the $x$ -axis. If the function lies below the $x$ -axis, then the area is negative. It is also defined as the antiderivative of a function.

Basic integrals

$\int x^n =\dfrac{x^{n+1}}{n+1}$

$\int_{a}^{b} f'(x)= f(b)-f(a)$

Properties of integrals

$\int_{a}^b f = \int_a^c f + \int_c^b f$

Other uses

The word integral is the adjectival form of the noun "integer." Thus, $3$ is integral while $\pi$ is not.

@@ Line 13: / Line 13: @@
 ==Other uses==
-The word ''integral'' is the adjectival form of the noun "[[integer]]."  Thus, <math>3</math> is integral while <math>\pi</math> is not.
+*The word ''integral'' is the adjectival form of the noun "[[integer]]."  Thus, <math>3</math> is integral while <math>\pi</math> is not.
-The word ''integral'' is also used in English to describe the state of being integrated; e.g., "The engine is an integral part of the vehicle -- without it, nothing would work."
 ==See also==

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Difference between revisions of "Integral"

Revision as of 21:03, 15 November 2007

Contents

Basic integrals

Properties of integrals

Other uses

See also