5.3 The Fundamental Theorem of Calculus/1: Difference between revisions
No edit summary |
No edit summary |
||
| Line 3: | Line 3: | ||
<math>\frac{d}{dx}\left[(x^2+1)^\frac{1}{2}+c\right]</math> | <math>\frac{d}{dx}\left[(x^2+1)^\frac{1}{2}+c\right]</math> | ||
let <math>a=x^2+1</math> and <math>b=a^{1/2}</math> then <math>\frac{da}{dx}=2x \text{and} \frac{db}{da}=\frac{1}{2}*a^{-1/2}</math> | let <math>a=x^2+1</math> and <math>b=a^{1/2}</math> then <math>\frac{da}{dx}=2x \text{ and } \frac{db}{da}=\frac{1}{2}*a^{-1/2}</math> | ||
Revision as of 19:31, 23 August 2022
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\frac{x}{\sqrt{x^2+1}}dx=\sqrt{x^2+1}+c}
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}\left[(x^2+1)^\frac{1}{2}+c\right]}
let 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 a=x^2+1} and 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=a^{1/2}} then 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{da}{dx}=2x \text{ and } \frac{db}{da}=\frac{1}{2}*a^{-1/2}}