The area bounded by the curves y= x, y= |x|, y=| x| and y=||x|| is [AIEEE 2002]

Correct Answer is : 4 sq. units

Correct Answer is : 4 sq. units

Test Index

AIEEE 2002 Math Solved Paper

Section: Mathematics

Question : 45 of 74

Marks: +1, -0

y=\ln x, y=\ln |x|, y=|\ln x|

y=|\ln|x||

Solution:

First we draw each curve as separate graph

NOTE : 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_{0}^{1}(-\ln x) dx

=-4 [x\ln x+-x_0^1] =4

sq. units

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