The area bounded between the parabola `y^(2)=4x` and the line y = 2x - 4 is equal to

Options

A. `(17)/(3)` sq units
B. `(19)/(3)` sq units
C. 9 sq units
D. 15 sq units

Answer

C

Explanation

The point of intersection of `y^(2)=4x` and y = 2x - 4 is `(2x-4)^(2)=4x`

`implies4x^(2)+16-16x=4x`
`implies 4x^(2)-20x+16=0`
`implies x^(2)-5x+4=0`
`rArr (x-1)(x-4)=0`
`rArr x=1,4rArry=-2,4`
`therefore` Required area `=int_(-2)^(4)((y+4)/(2))dy-int_(-2)^(4)(y^(2))/(4)dy`
`=(1)/(2)[(y^(2))/(2)+4y]_(-2)^(4)-(1)/(4)[(y^(3))/(3)]_(-2)^(4)`
`=(1)/(2)[8+16-(2-8)]-(1)/(12)[64+8]`
`=15-6=9` sq units