5.3 The Fundamental Theorem of Calculus/31

Evaluate the integral

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

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

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

Use FTC #2 $\int _{a}^{b}f(x)dt=F(b)-F(a)$