The area enclosed between the parabola `y = x^(2)-x+2` and the line y = x + 2 (in sq unit) equals to

Options

A. `8//3`
B. `1//3`
C. `2//3`
D. `4//3`

Answer

D

Explanation

Intersection points of given are (0,2) and (2,4)
`therefore` Required area `=int_(0)^(2)[(x+2)-(x^(2)-x+2)]dx`
`=int_(0)^(2)(-x^(2)+2x)dx`
`=[-(x^(3))/(3)+x^(2)]_(0)^(2)=-(8)/(3)+4=(4)/(3)` sq units