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Given \( f(x)=\int_{0}^{x} e^{t}\left(\log _{e} \sec t-\sec ^{2} t\right) d t, g(x)=-2 e^{x} \tan x \)
\( \mathrm{P} \) then the area bounded by the curves \( y=f(x) \) and \( y=g(x) \)

W between the ordinates \( x=0 \) and \( x=\frac{\pi}{3} \), is (in sq. units)
(1) \( \frac{1}{2} e^{\frac{\pi}{3}} \log _{e} 2 \)
(2) \( e^{\frac{\pi}{3}} \log _{e} 2 \)
(3) \( \frac{1}{4} e^{\frac{\pi}{3}} \log _{e} 2 \)
(4) \( e^{\frac{\pi}{3}} \log _{e} 3 \)
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