The area (in sq. units) of the region `{(x,y) in R^(2) : x^(2) le y le 2 +x}`, is :

Options

A. `(13)/(6)`
B. `9/2`
C. `(10)/(2)`
D. `(31)/(6)`

Answer

B

Explanation

`A={(lambda, 4) , x^(2) le y le x+2}`
`y ge x^(2)` and `y-x-2 le 0`
Point of intersection
`rArr x^(2)=x+2 rArr x^(2)-x -2=0`
`x=-1,2`

`A=[ underset(-1)overset(2)int ((x+2)-x^(2))dx=(x^(2))/(2)+2x-(x^(3))/(3)]_(-1)^(2)=(2+4-8/3)-(1/2-2 +1/3)`
`=8-3-1/2=5-1/2=9/2`