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

Options

A. `((5-4In2))/3`
B. `((2-In3))/2`
C. `((4-3In3))/2`
D. None of these

Answer

C

Explanation

`y=2-|2-x+={(x,:,xlt2),(4-x,:,xge2):}`
and `=3/(|x|)impliesy={(-3//x,:,xlt0),(3//x,:,xgt0):}`
`x=3/ximpliesx=sqrt(3)`

`4-x=3/x`
`impliesx=3(xgt2)`
`:.` Required area
`=int_(sqrt(3))^(2)(x-3/x)dx+int_(2)^(3)(4-x-3/x)dx`
`=(4-3log3)//2`