Let the straight line x=b divide the area enclosed by y=(1-x)^2, y=0 and x=0 into two parts R₁(0 x b) and R₂(b x 1) such that R₁-R₂= 1 4 . Then, b equals to

Step-by-step solution

Here, area between 0 to b is R₁ and b to aligned & 1 is R₂ & 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 & - 1 3 (1-b)^3-1 + 1 3 0-(1-b)^3 & = 1 4 aligned aligned & - 2 3 (1-b)^3=- 1 3 + 1 4 =- 1 12 & (1-b)^3= 1 8 & (1-b)= 1 2 b= 1 2 & aligned