5.3 The Fundamental Theorem of Calculus/11

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_{x}^{\pi}\sqrt{1+sec(t)}\cdot dt }

${\frac {d}{dx}}\left[g(x)\right]={\frac {d}{dx}}\left[\int _{x}^{\pi }{\sqrt {1+sec(t)}}\cdot dt\right]=0\cdot {\sqrt {1+sec(\pi )}}-1\cdot {\sqrt {1+sec(x)}}=-{\sqrt {1+sec(x)}}$

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 \text{Therefore, } g'(x)=-\sqrt{1+sec(x)}}