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  • Need clarity, kindly explain! Area bounded by y = tan-1x, y = cot-1x and y-axis is equal to

Area bounded by  y = tan-1x, y = cot-1x and y-axis is equal to

  • Option 1)

    \ln \;\sqrt 2  sq. units

  • Option 2)

    ln 4 sq. units

  • Option 3)

    ln 8 sq. units

  • Option 4)

    ln 2 sq. units

 

Answers (1)

best_answer

As we learnt 

 

Area between two curves -

 

If we have two functions intersection each other.First find the point of intersection.  Then integrate to find area

\int_{o}^{a}\left [ f\left ( x \right )-9\left ( x \right ) \right ]dx

- wherein

 

 Required area,

 

\Delta = \int\limits_0^{\pi /4} {\tan y\;dy + \int\limits_{\pi /4}^{\pi /2} {\cot y\;dy} } $

  = \ln \sec \left. {y\,} \right|_0^{\pi /4} + \ln \sin \left. y \right|_{5\pi /4}^{\pi /2}$

  = \ln \sqrt 2 - \ln \frac{1}{{\sqrt 2 }} = \ln 2$


Option 1)

\ln \;\sqrt 2 $ sq. units

Option 2)

ln 4 sq. units

Option 3)

ln 8 sq. units

Option 4)

ln 2 sq. units

Posted by

gaurav

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