Find the area of the region enclosed by ...

Find the area of the region enclosed by the parabola `x^(2)=y` and the line `y = x+ 2.`

A

`3/2`

B

`7/2`

C

`9/2`

D

`5/2`

Verified by Experts

The correct Answer is:

C

Area=`int_-1^2ydx`
=`int_-1^2((x+2)-(x^2))dx`
=`(x^2/2+2x-x^3/3)_-1^2`
=`(1/2(4-1)+2(2+1)-1/3(2^3+1))`
=`3/2+6-3`
=`9/2`

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