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Since either region is bounded by the parabola y=4x^{2} and a horizontal line (y=b and y=9), you should integrate the function
along the y-axis, not along the x-axis as usual. Solve the function for x and get x=½√y for x≥0. Due to the symmetry of the parabola, we do not need to integrate the other half of the parabola, x=-½√y for x≤0. We know that the area inside the parabola between y=0 and y=b is supposed to be half of the area inside the parabola between y=0 and y=9, which means

∫_{0}^{b} (½√y)dy = ½ ∫_{0}^{9} (½√y)dy.

Evaluate these two integrals and solve for b. You will get b=9/2^{2/3}≈5.67.