5.3 The Fundamental Theorem of Calculus/17: Difference between revisions

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FTC #1- <math>G(x)=f^\prime(x)</math>  or in other words <math>\frac{d}{dx}\left[\int\limits_{a(x)}^{b(x)}F(x)dx\right]</math> is <math>\ b^\prime(x)*f(b(x))-a^\prime(x)*f(a(x))</math>
<math>g(x)=\int_{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)=\frac{d}{dx}\left(\int\limits_{1-3x}^{1}\frac{u^3}{(1+u^2)} du\right) =(0)*f(1)-(-3)*f(1-3x)</math>
<math>g\prime(x)=\frac{d}{dx}\left(\int\limits_{1-3x}^{1}\frac{u^3}{(1+u^2)} du\right) =(0)*f(1)-(-3)*f(1-3x)</math>

Revision as of 20:21, 6 September 2022

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_{1-3x}^{1}\frac{u^3}{(1+u^2)} du}

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle g\prime (x)={\frac {d}{dx}}\left(\int \limits _{1-3x}^{1}{\frac {u^{3}}{(1+u^{2})}}du\right)=(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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