The area bounded by the curves
`xsqrt3+y=2log_(e)(x-ysqrt3)-2log_(e)2, y=sqrt3x,`
`y=-(1)/(sqrt3)x+2,` is

Options

A. `2log_(e)2` sq. units
B. `2log_(e)2+1` sq. units
C. `2log_(e)2-1` sq. units
D. `4log_(e)2-1` sq. units

Answer

C

Explanation

Rotating the system through an angle `60^(@)` in clock wise direction, the equations in the question become
`y=log_(e), x^(-)y=0,x=2`

Since after rotation the area remains unchanged
`"Required area"=int_(1)^(2)(log_(e)x)dx`
`=[xlog_(e)x-x]_(1)^(2)=[2log_(e)2-2]+1`