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

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FTC #1
FTC #1


<math>G(x)=f^\prime(x)</math>  or in other words <math>\frac{d}{dx}</math> of <math>\int\limits_{a(x)}^{b(x)}F(x)*dx</math> is <math>\ b(x)*f(b(x))-a(x)*f(a(x))</math>
<math>G(x)=f^\prime(x)</math>  or in other words <math>\frac{d}{dx}</math> of <math>\int\limits_{a(x)}^{b(x)}F(x)dx</math> is <math>\ b(x)*f(b(x))-a(x)*f(a(x))</math>


<math>y=\int\limits_{1-3x}^{1}\frac{x^3}{(1+u^2)} dx</math>
<math>y=\int\limits_{1-3x}^{1}\frac{x^3}{(1+u^2)} dx</math>

Revision as of 01:57, 24 August 2022

FTC #1

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}} 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://en.wikipedia.org/api/rest_v1/":): {\displaystyle \int\limits_{a(x)}^{b(x)}F(x)dx} 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(x)*f(b(x))-a(x)*f(a(x))}

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\limits_{1-3x}^{1}\frac{x^3}{(1+u^2)} dx}

so 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\limits_{1-3x}^{1}\frac{1}{(1+u^2)}x^3, dx}

using the formula we get y=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 (0)*f(1)-(-3)*f(1-3x)} 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*(1-3x)^3*\frac{1}{(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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