1. The problem statement, all variables and given/known data Let a > 0 be a fixed real number. Define A to be the area bounded between y=x2,y=2x2, and y=a2. Define B to be the area between y = x2, y = f(x), and x = a where f(x) is an unknown function. a) Show that if f(0) = 0, f(x) ≤ x2, and A = B then int 0-->a2 [y1/2-(y/2)1/2] dy = int 0--> a [x2 - f(x)] dx b) Find f(x) under the conditions above are true for all a > 0 2. Relevant equations I guess the equations for the lines, y=x2, y=2x2, y=a2 and y=x2, y=f(x), and x=a 3. The attempt at a solution The first thing I did was try to find the area A. A= int 0-->a2 [y1/2-(y/2)1/2] dy A= (2/3)y3/2 - (1/sqrt2)(2/3)y3/2| eval. 0 and a2 A= (2/3)a3 - (1/sqrt2)(2/3)a3 A= a3((2/3) - (1/sqrt2)(2/3)) a= (2/3)a3(1- (1/sqrt2)) Then I tried to find the area B, but this is where I got confused. B= int 0--> a [x2 - f(x)] dx B= [(1/3)x3|eval. 0-->a] - [int 0-->a [f(x)]] I don't see how I can go any farther, because I don't think I can integrate an unknown f(x). Am I going about this the wrong way?