anti-derivatives |
There are derivatives and there are antiderivatives. |
What is an antiderivative?If a derivative shows how a function changes, anti-derivatives must undo the change. Antiderivatives are found using integrals. There are definite integrals, which is bounded between an area and where the answer will result in a solid, numerical answer, (sometimes with units attached), and there are indefinite integrals, where the answer is a function with an attached + C to account for any unknown constants. (The exception to this is using differential equations to find C). This process is called integration.
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Integral notation
* This is the notation for the definite integral. We say, "Find the definite integral of [function]". For the answer, we say, "The definite integral of [said function] is [answer; w/ units if applicable]"
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** This is the notation for the definite integral. We say, "Find the definite integral of [function]". For the answer, we say, "The definite integral of [said function] is [answer; w/ units if applicable]"
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In the long run, integration is all about finding f(x) from f'(x) or finding f'(x) from f"(x), etc.
Example:
Example: