Difference between revisions of "Math 22 Antiderivatives and Indefinite Integrals"

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   The antidifferentiation process is also called integration and is denoted by <math>\int</math> (integral sign).
 
   The antidifferentiation process is also called integration and is denoted by <math>\int</math> (integral sign).
 
   <math>\int f(x)dx</math> is the indefinite integral of <math>f(x)</math>
 
   <math>\int f(x)dx</math> is the indefinite integral of <math>f(x)</math>
 +
 +
  If <math>F'(x)=f(x)</math> for all <math>x</math>, we can write:
 +
  <math>\int f(x)dx=F(x)+C</math> for <math>C</math> is a constant.
  
  

Revision as of 07:05, 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 , 
 it follows that 

 The antidifferentiation process is also called integration and is denoted by  (integral sign).
  is the indefinite integral of 

 If  for all , we can write:
 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 f(x)dx=F(x)+C}
 for 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 C}
 is a constant.


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