5.3 The Fundamental Theorem of Calculus/8: Difference between revisions
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<math> | <math> | ||
g(x)=\int_{3}^{x}e^{t^2-t}dt | g(x)=\int_{3}^{x}e^{t^2-t}dt \newline | ||
\frac{d}{dx}\left[g(x)\right] = \frac{d}{dx}\left[\int_{3}^{x}e^{t^2-t}dt\right]=1e^{x^2-x}-0e^{3^2-3}=e^{x^2-x} | \frac{d}{dx}\left[g(x)\right] = \frac{d}{dx}\left[\int_{3}^{x}e^{t^2-t}dt\right]=1e^{x^2-x}-0e^{3^2-3}=e^{x^2-x} | ||
\text{Therefore, } g'(x)=e^{x^2-x} | \text{Therefore, } g'(x)=e^{x^2-x} | ||
</math> | </math> | ||
Revision as of 20:30, 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 g(x)=\int_{3}^{x}e^{t^2-t}dt \newline \frac{d}{dx}\left[g(x)\right] = \frac{d}{dx}\left[\int_{3}^{x}e^{t^2-t}dt\right]=1e^{x^2-x}-0e^{3^2-3}=e^{x^2-x} \text{Therefore, } g'(x)=e^{x^2-x} }