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Antiderivative facts for kids

Kids Encyclopedia Facts

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 F and G.

In general, an antiderivative is written in the form \int f(x) \ dx, where:

  • The long S, \int, 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.
  • x is the equation you are integrating.
  • The letters dx mean "with respect to x". This tells you how to do the antidifferentiation.

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