The area ( in sq. units ) of the region A=\left \{ (x,y):\frac{y^{2}}{2}\leq x\leq y+4 \right \}  is :

  • Option 1)

    \frac{53}{3}

  • Option 2)

    30

  • Option 3)

    16

  • Option 4)

    18

 

Answers (1)

A=\left \{ (x,y):\frac{y^{2}}{2}\leq x\leq y+4 \right \}

required are

\\\int_{-2}^{4}\left ( y+4-\frac{y^{2}}{2} \right )dy\\\\\\\:=\frac{y^{2}}{2}+4y-\frac{y^{3}}{6}\:\:|^{4}_{-2}

 

=\left ( \frac{16}{2} +16-\frac{64}{6}\right )-\left ( \frac{4}{2}-8 +\frac{8}{6}\right )

=18

 


Option 1)

\frac{53}{3}

Option 2)

30

Option 3)

16

Option 4)

18

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