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  • Tell me? - If the area enclosed between the curves and,(k>0), is 1 sq. unit. Then k is : - Integral Calculus - JEE Main

If the area enclosed between the curves y = kx^{2} and x= ky^{2},(k>0), is 1 sq. unit. Then k is :

  • Option 1)

     

    \frac{\sqrt{3}}{2}

  • Option 2)

    \frac{1}{\sqrt{3}}

  • Option 3)

     

    \sqrt3

  • Option 4)

     

    \frac{2}{\sqrt3}

Answers (1)

best_answer

 

Area between two curves -

\\*I\! \! f \: f\left ( x \right )\geqslant g\left ( x \right )\\* in[a,c)\: \: and \: \: g\left ( x \right ) \geqslant f\left ( x \right )\:in(c,b]\\* Then\: area = \\*\\* \int_{a}^{c}\left ( f\left ( x \right )-g\left ( x \right ) \right )dx+\int_{c}^{b}\left ( g\left ( x \right )-f\left ( x \right ) \right )dx

- wherein

Area bounded by y^{2}=4ax  and  x^{2}=4by  is  \left | \frac{16ab}{3} \right |  (standard formula / result ) 

put 4a=\frac{1}{k}   and   4b=\frac{1}{k}

Area  =\left |\frac{16\cdot \frac{1}{4k}\cdot \frac{1}{4k}}{3} \right |=1

k=\frac{1}{\sqrt3}

 


Option 1)

 

\frac{\sqrt{3}}{2}

Option 2)

\frac{1}{\sqrt{3}}

Option 3)

 

\sqrt3

Option 4)

 

\frac{2}{\sqrt3}

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