The area (in sq. units) of the region A...

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

A

`(13)/(6)`

B

`9/2`

C

`(10)/(2)`

D

`(31)/(6)`

Verified by Experts

The correct Answer is:

B

`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`

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