5.3 The Fundamental Theorem of Calculus/15: Difference between revisions
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<math>\frac{d}{dx}\int_{a(x)}^{b(x)}f(t)\,dt=b^\prime | <math>\frac{d}{dx}\int_{a(x)}^{b(x)}f(t)\,dt=b^\prime{x}\cdot\,f(b(x))-\,a^\prime{x}\cdot\,f(a(x))</math> | ||
Revision as of 19:36, 25 August 2022
Use part 1 of the FTC to find the derivative of the function:
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 \begin{align} y=\int_{0}^{tan(x)}\sqrt{t+\sqrt t}\,dt =\sqrt{tan(x)+\sqrt tan(x)}\cdot\sec^{2}(x) \end{align} }
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 \frac{d}{dx}\int_{a(x)}^{b(x)}f(t)\,dt=b^\prime{x}\cdot\,f(b(x))-\,a^\prime{x}\cdot\,f(a(x))}