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}[\int\limits_{a(x)}^{b(x)}F(x)dx]</math> is <math>\ b^\prime(x)*f(b(x))-a^\prime(x)*f(a(x))</math> | ||
17)<math>y=\int\limits_{1-3x}^{1}\frac{u^3}{(1+u^2)} du</math> | |||
<math>y=\int\limits_{1-3x}^{1}\frac{u^3}{(1+u^2)} du</math> | |||
so using the formula we get y=<math>(0)*f(1)-(-3)*f(1-3x)</math> | so using the formula we get y=<math>(0)*f(1)-(-3)*f(1-3x)</math> | ||
Revision as of 18:52, 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))}
17)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 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*\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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