Question

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

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

Answer 1

Answer: (A)

4s units

Answer 2

First we draw each curve as separate graph undefined 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 $= 4 \int\limits^{1}_{0} (- \ell n x ) dx$ $= -4[x \,\ell\, n \, x - x]^1_0 = 4$ s units.