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The area bounded by the curve x=2-y-y^(2...

The area bounded by the curve `x=2-y-y^(2)` and Y-axis is

A

`(9)/(2)` sq unit

B

`(2)/(3)` sq unit

C

`(8)/(4)` sq units

D

`(5)/(3)` sq units

Text Solution

Verified by Experts

The correct Answer is:
A
At x = 0, `2-y-y^(2)=0`
`impliesy^(2)+y-2=0`
`implies y^(2)+2y-y-2=0`
`implies y(y+2)-(y+2)=0`
`implies(y+2)(y-1)=0`
implies y=-2,1
Therefore, the curve intersects y-axis at (0, 1) and (0, -2)
The required area `=int_(-2)^(1)xdy`

`=int_(-2)^(1)(2-y-y^(2))dy=[2y-(y^(2))/(2)-(y^(3))/(3)]_(-2)^(1)=(9)/(2)` sq units
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