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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.)

  • Calculus -

    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.

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