Difference between revisions of "Integral"
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| − | The '''integral''' is a generalization of [[area]]. The integral of a [[function]] is defined as the area between it and the <math>x</math>-axis. If the function lies below the <math>x</math>-axis, then the area is negative. | + | The '''integral''' is a generalization of [[area]]. The integral of a [[function]] is defined as the area between it and the <math>x</math>-axis. If the function lies below the <math>x</math>-axis, then the area is negative. It is also defined as the [[antiderivative]] of a function. |
==Basic integrals== | ==Basic integrals== | ||
| + | <math>\int x^n =\dfrac{x^{n+1}}{n+1}</math> | ||
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| + | <math>\int_{a}^{b} f'(x)= f(b)-f(a)</math> | ||
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==Properties of integrals== | ==Properties of integrals== | ||
Revision as of 11:10, 17 October 2007
The integral is a generalization of area. The integral of a function is defined as the area between it and the 
-axis. If the function lies below the -axis, then the area is negative. It is also defined as the antiderivative of a function.
Basic integrals
Properties of integrals
Other uses
The word integral is the adjectival form of the noun "integer." Thus, 
is integral while 
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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