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The area of the smaller region bounded b...

The area of the smaller region bounded by the circle `x^(2) + y^(2) =1` and the lines `|y| = x +1` is

A

`(pi-2)//4`

B

`(pi-2)//2`

C

`(pi+2)//2`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Due to symmetry,
Required area
` = 2 int_(-1)^(0) [sqrt(1-x^(2)) -(x+1)dx`
or area = 2
[area of sector `triangleOBA -triangle AOB]`
` = 2[(pi)/(4) -(1)/(2)] = ((pi-2))/(2)`
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