# Thread: Fundamental theorem of calc: trig functions

1. ## Fundamental theorem of calc: trig functions

anti-derivative((1-sin^2(theta))/(cos^2(theta)))d(theta) on the interval [0,pie/4] ????

sorry, I don't know the keys to put the symbols on the forum. thanks for any help.

2. Originally Posted by saiyanmx89
anti-derivative((1-sin^2(theta))/(cos^2(theta)))d(theta) on the interval [0,pie/4] ????

sorry, I don't know the keys to put the symbols on the forum. thanks for any help.
$\displaystyle \int\limits_0^{{\pi \mathord{\left/{\vphantom {\pi 4}} \right.\kern-\nulldelimiterspace} 4}} {\frac{{1 - {{\sin }^2}\left( \theta \right)}} {{{{\cos }^2}\left( \theta \right)}}} d\theta = \int\limits_0^{{\pi \mathord{\left/{\vphantom {\pi 4}} \right.\kern-\nulldelimiterspace} 4}} {\frac{{{{\cos }^2}\left( \theta \right)}}{{{{\cos }^2}\left( \theta \right)}}} d\theta =$$\displaystyle \left. {\int\limits_0^{{\pi \mathord{\left/ {\vphantom {\pi 4}} \right.\kern-\nulldelimiterspace} 4}} {d\theta } = \theta } \right|_0^{{\pi \mathord{\left/{\vphantom {\pi 4}} \right. \kern-\nulldelimiterspace} 4}} = \frac{\pi }{4}.$