The area bounded by the curve `y^(2)=1-x` and the lines `y=([x])/(x),x=-1, and x=(1)/(2)` is

Options

A. `(3)/(sqrt(2))-(11)/(6)` sq. units
B. `3sqrt(2)-(11)/(4)` sq. units
C. `(6)/(sqrt(2))-(11)/(5)` sq. units
D. None of these

Answer

A

Explanation

From the figure,
`A=overset(0)underset(-1)int(-1-(-sqrt(1-x)))dx+overset(1//2)underset(0)int(1-sqrt(1-x))dx`
`=[-x-((1-x)^(3//2))/(3//2)]_(-1)^(0)+[x+((1-x)^(3//2))/(3//2)]_(0)^(1//2)`
`=[-(2)/(3)-(1-(2xx2^(3//2))/(3))]+[(1)/(2)+(2)/(3xx2^(3//2))-(2)/(3)]`
`=(3)/(sqrt(3))-(4)/(3)-(1)/(2)`
`=(3)/(sqrt(2))-(11)/(6)` sq. units