The area inside the parabola `5x^(2)-y=0` but outside the parabola `2x^(2)-y+9=0` is

Options

A. `12sqrt(3)` sq. units
B. `6sqrt(3)` sq. units
C. `8sqrt(3)` sq. units
D. `4sqrt(3)` sq. units

Answer

A

Explanation

`"Given "5x^(2)-y=0" ...(1)"`
`"and "2x^(2)-y+9=0" ...(2)"`
`5x^(2)-(2x^(2)+9)=0`
`"or "3x^(2)=9 or x=-sqrt(3),sqrt(3)`
`therefore" Required area "=2int_(0)^(sqrt(3))((2x^(2)+9)-5x^(2))dx`
`=2int_(0)^(sqrt(3))(9-3x^(2))dx`
`=2[9x-x^(3)]_(0)^(sqrt(3))`
`=2[9sqrt(3)-3sqrt(3)]`
`=12sqrt(3)` sq. units