Let the straight line x= b divide the area enclosed by `y=(1-x)^(2),y=0, and x=0` into two parts `R_(1)(0lexleb) and R_(2)(blexle1)` such that `R_(1)-R_(2)=(1)/(4).` Then b equals

Options

A. `3//4`
B. `1//2`
C. `1//3`
D. `1//4`

Answer

B

Explanation

`because" "overset(b)underset(0)int(1-x^(2))dx-overset(1)underset(b)int(1-x)^(2)dx=(1)/(4)`

`rArr" "(x-1)^(2)/(3):|_(0)^(b)-(x-1)^(3)/(3):|_(b)^(1)=(1)/(4)`
`rArr" "(b-1)^(3)/(3)+(1)/(3)-(0-(b-1)^(3)/(3))=(1)/(4)`
`"or "(2(b-1)^(3))/(3)=-(1)/(12)`
`"or "(b-1)^(3)=-(1)/(8) or b=(1)/(2)`