The area bounded by the curves y=\ln x, \; y=\ln \left | x \right |,\; y=\left | \ln x \right |\; and\; y=\left |\ln \right |x\|\; is

  • Option 1)

    4 sq. units

  • Option 2)

    6 sq. units

  • Option 3)

    10 sq. units

  • Option 4)

    none of these

 

Answers (1)

As we learnt in

Area along y axis -

Let y_{1}= f_{1}(x)\, and \, y_{2}= f_{2}(x) be two curve, then area bounded by the curves and the lines

y = a and y = b is

A=\int_{a}^{b}\left ( x_{2}-x_{1} \right )dy

- wherein

 

 Area bound==4\int_{0}^{1}1.ln\ x\:dx

=4\left [ x\:ln\ x-x \right ]_{0}^{1}

=4\times 1=4\ sq\ units


Option 1)

4 sq. units

This option is correct 

Option 2)

6 sq. units

This option is incorrect 

Option 3)

10 sq. units

This option is incorrect 

Option 4)

none of these

This option is incorrect 

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