Correct Answer - B
The smaller bounded by the circle `x^(2)+y^(2)=4` and the line `x+y=2` is shown by the shaded region ACBA.
The points of intersection of the circle and line are A(2, 0) and B(0, 2).
` :.` Required area (shaded region).
`=ar(OACBO)-ar(triangle OAB)`
`=int_(0)^(2)sqrt(4-x^(2))dx-int_(0)^(2)(2-x)dx`
`=[(x)/(2)sqrt(4-x^(2))+(4)/(2)"sin"^(-1)(x)/(2)]_(0)^(2)-[2x-(x^(2))/(2)]_(0)^(2)`
`=[(2)/(2)sqrt(4-4)+(4)/(2)"sin"^(-1)(1)-0-(4)/(2)"sin"^(-1)(0)]-[4-2]`
`=[2*(pi)/(2)]-[4-2]=(pi-2)` sq. units.