5.3 The Fundamental Theorem of Calculus/11
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Revision as of 19:24, 25 August 2022 by Elizabethh58413 (talk | contribs) (Created page with "<math> g(x)= \int_{\pi}^{x}\sqrt{1+sec(t)}\cdot dt </math> <br><br> <math> \frac{d}{dx}\left[g(x)\right]=\frac{d}{dx}\left[\int_\pi^{x}\sqrt{1+sec(t)}\cdot dt\right]=0 \cdot \sqrt{1+sec(\pi)} - 1\cdot \sqrt{1+sec(x)} = -\sqrt{1+sec(x)}</math> <br><br> <math>\text{Therefore, } g'(x)=-\sqrt{1+sec(x)}</math>")
![{\displaystyle {\frac {d}{dx}}\left[g(x)\right]={\frac {d}{dx}}\left[\int _{\pi }^{x}{\sqrt {1+sec(t)}}\cdot dt\right]=0\cdot {\sqrt {1+sec(\pi )}}-1\cdot {\sqrt {1+sec(x)}}=-{\sqrt {1+sec(x)}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/7c6f9d7c2454ffdfc1e638bcf95003f4f408e5df)
