5.3 The Fundamental Theorem of Calculus/31

Evaluate the integral

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_{0}^\frac{\pi}{4}sec^{2}(t)dt }

$\int _{0}^{\frac {\pi }{4}}sec^{2}(t)dt=tan({\frac {\pi }{4}})-tan(0)=1-0=1$

Therefore, Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int _{0}^{\frac {\pi }{4}}sec^{2}(t)dt=1}

(Use FTC #2, Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int _{a}^{b}f(x)dt=F(b)-F(a)} )