Question

The area bounded by the curves y = lnx, y = ln |x|,y = | ln x | and y = | ln |x| | is

• A. 4sq. units
• B. 6 sq. units
• C. 10 sq. units
• D. none of these

Answer 1

Answer: (A)

First we draw each curve as separate graph

Graph of y = | f(x) | can be obtained from the graph of the curve y = f(x) by drawing the mirror image of the portion of the graph below x-axis, with respect to x-axis.
Clearly the bounded area is as shown in the following figure.

Required area $=4\underset{0}{\overset{1}{\int }}(-\ell nx)dx$
$=-4[x\ell nx-x{]}_0^1=4$ sq. units.