5.3 The Fundamental Theorem of Calculus/17: Difference between revisions
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<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 01:51, 24 August 2022
FTC #1
Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\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}} 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}
=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)}
=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)}x^3+c}