The area of the region bounded by the x-axis | vedclass

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(A) The function $y = 	an x$ is an odd function,meaning $f(-x) = -f(x)$.Since the interval $(-\pi/3, \pi/3)$ is symmetric about the origin,the area i

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$2 \log 2$

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(A) The function $y = 	an x$ is an odd function,meaning $f(-x) = -f(x)$.Since the interval $(-\pi/3, \pi/3)$ is symmetric about the origin,the area is given by $2 	imes \int_0^{\pi/3} 	an x \, dx$.Evaluating the integral: $2 \int_0^{\pi/3} 	an x \, dx = 2 [\log |\sec x|]_0^{\pi/3}$.Substituting the limits: $2 (\log |\sec(\pi/3)| - \log |\sec(0)|) = 2 (\log 2 - \log 1)$.Since $\log 1 = 0$,the result is $2 \log 2$.

The area of the region bounded by the $x$-axis and the curves defined by $y = \tan x$ for $(-\pi/3 \le x \le \pi/3)$ is

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