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

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FTC #2 (not done yet)


<math>\int\limits_{a}^{b}f(x)dx</math> is equal to <math>F(b)-F(a)</math> Where F is the antiderivative of f such that <math>F^\prime=f</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 18:44, 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}[\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^\prime(x)*f(b(x))-a^\prime(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{u^3}{(1+u^2)} du}

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)}u^3, du}

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)}

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*(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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