Question

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

• A. $\log\sqrt{2}$
• B. $- \log\sqrt{2}$
• C. $2\log 2$
• D. 0

Answer 1

Answer: (C)

$2\log 2$

Answer 2

Required area

$= 2\int_{0}^{\pi/3}{\tan xdx} = 2\lbrack{logsec}x\rbrack_{0}^{\pi/3} = 2\log(2)$.