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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 ln 2)/3)` sq unit

B

`((2-ln 3)/2)` sq unit

C

`((4-3 ln3)/2)` sq unit

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`y =2-abs(2-x),y = 3/absx`
`y ={{:(x",",x le2),(4-x",",xge2):}y = {{:(3/x",",xgt0),(-3/x",",xlt0):}`
Hence, required area
`PQRSP = "area" PQRP + " area" PRSP`
`=abs(int_(sqrt3)^2(x-3/x)dx) + abs(int_2^3((4-x) -3/x)dx) = (4-3 ln 3)/2` sq unit.
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