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? asked in Science & MathematicsMathematics · 1 decade ago

Please find the area of the surface by rotating around the curve?

Find the area of the surface obtained by rotating the curve x = 1+2y^2 from y=1 to y = 2 about the x-axis.

Please help please!

1 Answer

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  • GusBsAs
    Lv 6
    1 decade ago
    Favorite Answer

    dS = 2 π y dL

    dL = √(dx²+dy²) = √(16 y² + 1) dy =>

    S = 2 π ∫(from 1 to 2) y √(16 y² + 1) dy

    u = 16 y² + 1

    du = 32 y dy

    =>

    S = 2 π (1/32) ∫(from 17 to 65) √u du =

    = (π/16) (2/3) [65^(3/2) - 17^(3/2)] =

    = (π/24) [65^(3/2) - 17^(3/2)]

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