Consider two curves `C_1: y=1/x a n dC_2: y=1nx` on the `x y` plane. Let `D_1` denotes the region surrounded by `C_1,C_2,` and the line `x=1a n dD_2` denotes the region surrounded by `C_1,C_2` and the line `x=adot` If `D_1=D_2,` then the sum of logarithm of possible value of `a` is _____________

Options

A. 1 sq. units
B. 2 sq. units
C. `2+sqrt(3)` sq. units
D. None of these

Answer

B

Explanation

`overset(pi//6)underset(0)int((1+cosx)-(1+cos (x-(pi)/(3))))dx+overset(pi)underset(pi//6)int((1+cos (x-(pi)/(3)))-(1+cos x))dx`
`=[ sin x- sin (x-(pi)/(3))]_(0)^(pi//6)+[sin(x-(pi)/(3))- sin x]_(pi//6)^(pi)`
`=[((1)/(2)+(1)/(2))-(sqrt(3))/(2)]+[(sqrt(3))/(2)-(-(1)/(2)-(1)/(2))]`
`=2` sq. units.