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The area bended by the curve y=x^(2)+2,y...

The area bended by the curve `y=x^(2)+2,y=x,x=3` and y-axis is

A

`(9)/(2)` sq unit

B

9 sq unit

C

21 sq unit

D

`(21)/(2)` sq unit

Text Solution

Verified by Experts

The correct Answer is:
D

The point of intersection of the curve `y = x^(2)+2` and the line x = 3 is (3, 11).
Required area (shown in shaded region)
= Area OABDO - Area OCDO
= [Area under `y = x^(2)+2` between x =0, x = 3] - [Area under y = x between x = 0, x = 3]
`=int_(0)^(3)(x^(2)+2)dx-int_(0)^(3)xdx=[(x^(3))/(3)+2x]_(0)^(3)-[(x^(2))/(2)]_(0)^(3)`
`=[(3^(3))/(3)+6-0]-[(3^(2))/(2)-0]`
`=9+6-(9)/(2)=(21)/(2)` sq units
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