The area (in sq. units) of the region  A=\left \{ \left ( x,y \right ):x^{2}\leq y\leq x+2 \right \} is :

  • Option 1)

    \frac{10}{3}

  • Option 2)

    \frac{9}{2}

  • Option 3)

     \frac{31}{6}

  • Option 4)

     \frac{13}{6}

 

Answers (1)

Point of intersection of x^{2}=y and y=x+2

                                      \left ( -1,1 \right ) and \left ( 2,4 \right )

           y=x+2

                                         Required Area,

                              =\int_{-1}^{2}\left ( x+2-x^{2} \right )dx

                             =\left [ \frac{x^{2}}{2}+2x-\frac{x^{3}}{3} \right ]^{2}_{-1}

                               =\frac{9}{2}                   

 


Option 1)

\frac{10}{3}

Option 2)

\frac{9}{2}

Option 3)

 \frac{31}{6}

Option 4)

 \frac{13}{6}

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