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Thread: Fundamental theorem of calc: trig functions

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    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.
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    Quote Originally Posted by saiyanmx89 View Post
    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}.$
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