1. The problem statement, all variables and given/known data Find the parabola y=a(x^2) that divides the area under the curve y=x(1-x) over [0,1] into two regions of equal area. 2. Relevant equations I set the two equations equal to each other to solve that the intersection point is x=1/(1+a). I solved for the entire area "definite integral x(1-x) from [0,1] dx" = 1/6. 3. The attempt at a solution I attempt half the area with the two definite integrals "a(x^2) from [0,(1/(1+a))]" + the integral "x(1-x) from [(1/(1+a)), 1]" set equal to 1/12 (half the area). But I can not solve for a. It looks like there is Linear algebra but I am only in a Calc II class so it should not be too hard. Please help.