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Find the area of the region enclosed by ...

Find the area of the region enclosed by the parabola `x^2=y," the line " y=x+2` and the X-axis.

A

`3/2`

B

`7/2`

C

`9/2`

D

`5/2`

Text Solution

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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