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Let f(x)= minimum (x+1,sqrt(1-x)) for al...

Let `f(x)=` minimum `(x+1,sqrt(1-x))` for all `xle1`. Then the area bounded by `y=f(x)` and the x-axis is k units then 6 k is equal to

A

`(7)/(3)` sq. units

B

`(1)/(6)` sq. units

C

`(11)/(6)` sq. units

D

`(7)/(6)` sq. units

Text Solution

Verified by Experts

The correct Answer is:
D

Required area =Shaded region
`=overset(1)underset(0)int(x_(2)-x_(1))dy` (integrating along y-axis)
`=overset(1)underset(0)int[(1-y^(2))-(y-1)]dy`
`=(7)/(6)` sq. unit
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