5.3 The Fundamental Theorem of Calculus/37: Difference between revisions
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FTC # 2- the <math>\frac{d}{dx}[\int\limits_{a(x)}^{b(x)}F(x)dx]</math> is F(b)-F(a) where F is the antiderivitive of f such that <math>F^\prime=f</math> | FTC # 2- the <math>\frac{d}{dx}[\int\limits_{a(x)}^{b(x)}F(x)dx]</math> is F(b)-F(a) where F is the antiderivitive of f such that <math>F^\prime=f</math> | ||
37) <math>\int\limits_{1/2}^{ | 37) <math>\int\limits_{1/2}^{\sqrt{3})/2}\frac{6}{(\sqrt{1-t^2})} dt </math> | ||
using the rule we get | using the rule we get | ||
<math>6sin^-1(x)\bigg|_{1/2}^{\sqrt{3} | <math>6sin^-1(x)\bigg|_{1/2}^{\sqrt{3}/2}</math> | ||
[[5.3 The Fundamental Theorem of Calculus/1|1]] | [[5.3 The Fundamental Theorem of Calculus/1|1]] | ||
Revision as of 19:04, 25 August 2022
FTC # 2- the 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 F(b)-F(a) where F is the antiderivitive of f such that 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 F^\prime=f}
37) Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int \limits _{1/2}^{{\sqrt {3}})/2}{\frac {6}{({\sqrt {1-t^{2}}})}}dt}
using the rule we get 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 6sin^-1(x)\bigg|_{1/2}^{\sqrt{3}/2}}
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