The area bounded by `y = 3-|3-x|` and `y=6/(|x+1|)` is

Options

A. `(15)/(2)-6" In "2` sq. units
B. `(13)/(2)-3" In "2` sq. units
C. `(13)/(2)-6" In "2` sq. units
D. None of these

Answer

C

Explanation

First consider `y=3-|3-x|`
`"For "xlt3,y=3-(3-x)=x`
`"For "xge3,y=3-(x-3)=6-x`
`"Consider "y=(6)/(|x+1|)`
`"For "xlt-1," "y=(6)/(-1-x)`
`rArr" "(1+x)y=-6`
`"For "xgt-1, y=(6)/(x+1)`
`"Required area "=[overset(3)underset(2)int(x-(6)/(x+1))dx+overset(5)underset(3)int((6-x)-(6)/(x+1))dx]`
`=[((x^(2))/(2))_(2)^(3)+(6x-(x^(2))/(2))_(3)^(5)-(6log (x+1))_(2)^(5)]`
`=[(5)/(2)+4-6log2\]`
`=(13)/(2)-6" In "2` sq. units.