1.

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

Answer» We can draw graphs for these `4` curves.
Please refer to the video to see the graphs.
The common intersection area is the required area.
From the graph, we can see that,
Area of shaded region `(A)= 4 int_(-oo)^0 xdy`
Now, `y = lnx => x = e^y``:. A = 4 int_(-oo)^0 e^y dy`
`=>A = 4[e^y]_(-oo)^0`
`=>A = 4[e^0 - e^(-oo)]`
`=>A = 4[1-0]`
`=>A = 4`
So, area bounded by the given curves is `4` square units.


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