The area bounded by `y = 2-|2-x| and y=3/|x|` is:

Options

A. `((5-4"In"2)/(3))`sq unit
B. `((2-"In"3)/(2))` sq unit
C. `((4-3"In"3)/(2))` sq unit
D. none of these

Answer

C

Explanation

`y=2-|2-x|, y=(3)/(|x|)`
`y={(x",",x le2),(4-x",",x ge2):},y={((3)/(x) ",",x gt0),(-(3)/(x)",",x lt 0):}`
Hence, required area
PQRSP = area PQRP + area PRSP
`=|int_(sqrt(3))^(2)(x-(3)/(x))dx|+ |int_(2)^(3)((4-x)-(3)/(x))dx| =(4-3"In"3)/(2)` sq unit.