Fundamental theorem of calc: trig functions

**saiyanmx89** · January 19th 2009, 11:50 AM

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.

**DeMath** · January 19th 2009, 12:00 PM

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.

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

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