Difference between revisions of "Math 22 Antiderivatives and Indefinite Integrals"
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==Antiderivatives== | ==Antiderivatives== | ||
| − | A function <math>F</math> is an antiderivative of a function <math>f</math> when for every <math>x</math> in the domain of <math>f</math>, it follows that <math>F'(x)=f(x)</math> | + | A function <math>F</math> is an antiderivative of a function <math>f</math> when for every <math>x</math> in the domain of <math>f</math>, |
| + | it follows that <math>F'(x)=f(x)</math> | ||
| + | The antidifferentiation process is also called integration and is denoted by <math>\int</math> | ||
Revision as of 07:02, 12 August 2020
Antiderivatives
A function Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F}
is an antiderivative of a function Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f}
when for every Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x}
in the domain of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f}
,
it follows that
The antidifferentiation process is also called integration and is denoted by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int}
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