# Fundamental theorem of calc: trig functions

• Jan 19th 2009, 11:50 AM
saiyanmx89
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.
• Jan 19th 2009, 12:00 PM
DeMath
Quote:

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.

$\int\limits_0^{{\pi \mathord{\left/{\vphantom {\pi 4}} \right.\kern-\nulldelimiterspace} 4}} {\frac{{1 - {{\sin }^2}\left( \theta \right)}}
{{{{\cos }^2}\left( \theta \right)}}} d\theta = \int\limits_0^{{\pi \mathord{\left/{\vphantom {\pi 4}} \right.\kern-\nulldelimiterspace} 4}} {\frac{{{{\cos }^2}\left( \theta \right)}}{{{{\cos }^2}\left( \theta \right)}}} d\theta =$
$\left. {\int\limits_0^{{\pi \mathord{\left/
{\vphantom {\pi 4}} \right.\kern-\nulldelimiterspace} 4}} {d\theta } = \theta } \right|_0^{{\pi \mathord{\left/{\vphantom {\pi 4}} \right.
\kern-\nulldelimiterspace} 4}} = \frac{\pi }{4}.$