Question

The area bounded by the curves y = log_ex, y = log_e|x|,

y = |log_e x| and y = |log_e |x|| is

• A. 5 sq. units
• B. 2 sq. units
• C. 4 sq. units
• D. None

Answer 1

Answer: (C)

4 sq. units

Answer 2

So area bounded by four curve

Apply L'Hospital rule

$\lim _ { x \rightarrow 0 }$ (x log x – x)

$\lim _ { x \rightarrow 0 }$ (¥/¥)

$\lim _ { x \rightarrow 0 }$ = $\lim _ { x \rightarrow 0 }$ (–x) = 0

So area = = 4

$\left| 1 - \lim _ { x \rightarrow 0 } ( x \log x - x ) \right|$

= 4 |1 – 0| = 4 sq. units.