5.3 The Fundamental Theorem of Calculus/17: Difference between revisions
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17) <math>g(x)=\int\limits_{1-3x}^{1}\frac{u^3}{(1+u^2)} du</math> | 17) <math>g(x)=\int\limits_{1-3x}^{1}\frac{u^3}{(1+u^2)} du</math> | ||
<math>g\prime(x)=(0)*f(1)-(-3)*f(1-3x)</math> | <math>g\prime(x)=d/dx(\int\limits_{1-3x}^{1}\frac{u^3}{(1+u^2)} du) =(0)*f(1)-(-3)*f(1-3x)</math> | ||
which is equal to <math>(3)*f(1-3x)</math> | which is equal to <math>(3)*f(1-3x)</math> | ||
Revision as of 19:26, 25 August 2022
FTC #1- 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://en.wikipedia.org/api/rest_v1/":): {\displaystyle G(x)=f^\prime(x)} or in other words 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://en.wikipedia.org/api/rest_v1/":): {\displaystyle \frac{d}{dx}\left[\int\limits_{a(x)}^{b(x)}F(x)dx\right]} is 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://en.wikipedia.org/api/rest_v1/":): {\displaystyle \ b^\prime(x)*f(b(x))-a^\prime(x)*f(a(x))}
17) 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://en.wikipedia.org/api/rest_v1/":): {\displaystyle g(x)=\int\limits_{1-3x}^{1}\frac{u^3}{(1+u^2)} du}
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://en.wikipedia.org/api/rest_v1/":): {\displaystyle g\prime(x)=d/dx(\int\limits_{1-3x}^{1}\frac{u^3}{(1+u^2)} du) =(0)*f(1)-(-3)*f(1-3x)}
which is equal to 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://en.wikipedia.org/api/rest_v1/":): {\displaystyle (3)*f(1-3x)}
which is=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://en.wikipedia.org/api/rest_v1/":): {\displaystyle 3*\frac{(1-3x)^3}{(1+(1-3x)^2)}}
or simplified to 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://en.wikipedia.org/api/rest_v1/":): {\displaystyle \frac{3*(1-3x)^3}{(1+(1-3x)^2)}}
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