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  1. #1
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    How do you do this?

    Find the number b such that the line y = b divides the region bounded by the curves y=3x^2 and y = 2 into two regions with equal area.

    Enter your answer either as a expression or as a decimal rounded to four places.
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  2. #2
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    Quote Originally Posted by asnxbbyx113 View Post
    Find the number b such that the line y = b divides the region bounded by the curves y=3x^2 and y = 2 into two regions with equal area.

    Enter your answer either as a expression or as a decimal rounded to four places.
    Hi,

    for convenience I only consider the area in the first quadrant, that means x ≥ 0.

    from y = 3x you get x = √(y/3)

    The area in question is: int from(0) to(2) √(y/3) dy = √(1/3)*((2/3)*y^(3/2)) from(0) to(2) = (4/3)*(√(2/3))

    So the complete area is (8/3)*(√(2/3)) ≈ 2.1773... square-units

    I consider now the half of the area in the first quadrant:

    (2/3)*(√(2/3)) = int from(0) to(b) (√(y/3))dy = √(1/3)*((2/3)*y^(3/2)) from(0) to(b) = (2/3)*√(1/3)*√(b).
    Divide both sides by (2/3) and square both sides. Solve for b. I've got:

    b = √(2) ≈ 1.2599..

    EB
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