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

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<math>g(x)=\int_{1-3x}^{1}\frac{u^3}{(1+u^2)} du</math>
<math>y=\int_{1-3x}^{1}\frac{u^3}{1+u^2} du</math>




<math>
<math>
\frac{d}{dx}(g(x))=\frac{d}{dx}\left(\int_{1-3x}^{1}\frac{u^3}{(1+u^2)} du\right) = (0)\cdot\frac{(1)^3}{(1+(1)^2)}
\frac{d}{dx}(y)=\frac{d}{dx}\left(\int_{1-3x}^{1}\frac{u^3}{(1+u^2)} du\right) = (0)\cdot\frac{(1)^3}{(1+(1)^2)}


-(-3)\cdot\frac{(1-3x)^3}{(1+(1-3x)^2)}
-(-3)\cdot\frac{(1-3x)^3}{(1+(1-3x)^2)}
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<math>
<math>
\text{Therefore, } g'(x) = \frac{3(1-3x)^3}{1+(1-3x)^2}
\text{Therefore, } y' = \frac{3(1-3x)^3}{1+(1-3x)^2}
</math>
</math>

Revision as of 20:30, 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 y=\int_{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 \frac{d}{dx}(y)=\frac{d}{dx}\left(\int_{1-3x}^{1}\frac{u^3}{(1+u^2)} du\right) = (0)\cdot\frac{(1)^3}{(1+(1)^2)} -(-3)\cdot\frac{(1-3x)^3}{(1+(1-3x)^2)} }


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 \text{Therefore, } y' = \frac{3(1-3x)^3}{1+(1-3x)^2} }

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