Tính y = |f(x) 3sin(a) 4cos(a)|

\(\int\limits_0^{\frac{\pi }{4}} {\frac{{3{{\sin }^2}x - 4{{\cos }^2}x}}{{{{\cos }^2}x}}dx} \)

\( = \int\limits_0^{\frac{\pi }{4}} {\frac{{3\left( {1 - {{\cos }^2}x} \right) - 4{{\cos }^2}x}}{{{{\cos }^2}x}}dx} \)

\( = \int\limits_0^{\frac{\pi }{4}} {\frac{{3 - 3{{\cos }^2}x - 4{{\cos }^2}x}}{{{{\cos }^2}x}}dx} \)

\( = \int\limits_0^{\frac{\pi }{4}} {\frac{{3 - 7{{\cos }^2}x}}{{{{\cos }^2}x}}dx} \)

\( = \int\limits_0^{\frac{\pi }{4}} {\frac{3}{{{{\cos }^2}x}} - 7dx} \)

\[ = \left. {3\tan x - 7x} \right|_0^{\frac{\pi }{4}}\]

\[ = \left( {3\tan \left( {\frac{\pi }{4}} \right) - 7.\frac{\pi }{4}} \right) - 3\tan \left( 0 \right) - 7.0\]

\( = 3 - \frac{{7\pi }}{4}\)