If the straight-line x=b divides the area enclosed by y=(1-x)_ - ^2y=0 and x=0 in two parts R₁(0 x b) and R₂(b x 1) such that R₁-R₂= 1 4 . Then b equals

Step-by-step solution

aligned & ₀^b(1-x)^2 ~d x- _b^1(1-x)^2 ~d x= 1 4 & [ (1-x)^3 -3 ]₀^b- [ (1-x)^3 -3 ]_b^1= 1 4 aligned aligned & (1-b)^3-(1-0)^3-(1-1)^3+(1-b)^3 -3 = 1 4 & 2(1-b)^3-1= -3 4 & 2(1-b)^3-1= -3 4 & (1-b)^3= 1 8 & b= 1 2 aligned