Find the number b such that the line y = b divides the region bounded by the curves y = 4x2 and y = 1 into two regions with equal area. (Round your answer to two decimal places.)

Answer 1

We need the whole area to be twice the
area under the line y=b.

y(1/2) = 1
y(√b/2) = b

So, integrating along x, we need

∫[0,1/2] 1-4x^2 dx = 2∫[0,√b/2] b-4x^2 dx

Now just evaluate the integrals and solve the polynomial for b.