The area of the region bounded between the curves `y=e||x|In|x||,x^2+y^2-2(|x|+|y|)+1>=0` and X-axis where `|x|<=1`, if `alpha` is the x-coordinate of the point of intersection of curves in 1st quadrant, is

Options

A. `4[int_(0)^alpha ex In x dx+int_(alpha)^(1)(1-sqrt(1-(x-1)^2))dx]`
B. `4[int_(0)^alpha ex In x dx+int_(1)^(alpha)(1-sqrt(1-(x-1)^2))dx]`
C. `4[-int_(0)^alpha ex In x dx+int_(alpha)^(1)(1-sqrt(1-(x-1)^2))dx]`
D. `2[int_(0)^alpha ex In x dx+int_(alpha)^(1)(1-sqrt(1-(x-1)^2))dx]`

Answer

D