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The area bounded by y = 2-|2-x| and y=3/...

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

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

Text Solution

Verified by Experts

The correct Answer is:
C

`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.
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