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If the area (in sq. units) of the region...

If the area (in sq. units) of the region
`{(x,y): y^(2) gt= 4x,x+y lt=1,xgt=0,ygt=0}` is `asqrt2+b`, then `a-b` is equal to :

A

`(8)/(3)`

B

`(10)/(3)`

C

`-(2)/(3)`

D

6

Text Solution

Verified by Experts

The correct Answer is:
D
`A=int_(0)^(2sqrt2-2)(1-y(y^(2))/(4))dy`
`A=[y-(y^(2))/(2)-(y^(3))/(12)]_(0)^(2sqrt2-2)=y[1-(y)/(2)-(y^(2))/(12)]`
`=2(sqrt2-1)[1-(sqrt2-1)-(4)/(12)(sqrt2-1)^(2)]`
`=2(sqrt2-1)[2-sqrt2-(1)/(3)(2+1-2sqrt2)]`
`=2(sqrt2-1)[1-(sqrt2)/(3)]=2(sqrt2-(2)/(3)=1+(sqrt3)/(3))`
`=2((4)/(3)sqrt2-(5)/(3))`
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