The area bounded by the curve y = x, x = -()/6, x = ()/6 and y=0 is Option 1: _e4/3 Sq. units Option 2: _e2/3 Sq. units Option 3: _e2/(3) Sq. units Option 4: _e 2 Sq. units

Answer: _e4/3 Sq. units. Solution: Since, x, is even, area =2_0^(/6) x dx = 2[_e x]_0^(/6). =2_e2/(3)=_e4/3 square units.

Calculus

Application of Integrals

Medium

core

The area bounded by the curve $y = \tan x$ , $x = -\dfrac{\pi}{6}, x = \dfrac{\pi}{6}$ and $y=0$ is

$\log_e\dfrac{4}{3}$ Sq. units

$\log_e\dfrac{2}{3}$ Sq. units

$\log_e\dfrac{2}{\sqrt3}$ Sq. units

$\log_e 2$ Sq. units

✅ Correct Option: 1

Since $|\tan x|$ is even, area $=2\int_0^{\pi/6}\tan x\,dx = 2[\log_e\sec x]_0^{\pi/6}$ .

$=2\log_e\dfrac{2}{\sqrt3}=\log_e\dfrac{4}{3}$ square units.

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