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Q.
The area bounded by the curves y = lnx, y = ln |x|,y = | ln x | and y = | ln |x| | is
Application of Integrals
Solution:
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 \int\limits^{1}_{0} (- \ell n x ) dx $
$ = -4[x \,\ell\, n \, x - x]^1_0 = 4$ sq. units.
