Antiderivative facts for kids

Antidifferentiation (also called indefinite integration) is the process of finding a certain function in calculus. It is the opposite of differentiation. It is a way of processing a function to give another function (or class of functions) called an antiderivative. Antidifferentiation is like integration—but without limits. This is why it is called indefinite integration. When represented as single letters, antiderivatives often take the form of capital roman letters such as and .

In general, an antiderivative is written in the form , where:

• The long S, , is called an integral sign. In integration, the integral sign has numbers on it. Those numbers tell you how to do the integration. Antiderivatives are different. They do not have numbers on on their integral signs.
• is the equation you are integrating.
• The letters mean "with respect to ". This tells you how to do the antidifferentiation.

Related pages

• Fundamental theorem of calculus
• Integral
• Numerical integration
• Partial fraction decomposition

Images for kids

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  The slope field of F(x) = \frac{x^3}{3}-\frac{x^2}{2}-x+c, showing three of the infinitely many solutions that can be produced by varying the arbitrary constant c.

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  Figure 1.

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  Figure 2.

See also

In Spanish: Integración indefinida para niños