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March 29, 2017

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Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.
y=x^2,x=y^2 about the axis x=–7

  • Calculus - ,

    using discs (washers)

    v = ∫[0,1] π(R^2-r^2) dy
    where R = 7+√y and r = 7+y^2
    v = π∫[0,1] (7+√y)^2 -(7+y^2)^2) dy
    v = 149π/30

    using shells
    v = ∫[0,1] 2πrh dx
    where r = 7+x and h = √x-x^2
    v = 2π∫[0,1] (7+x)(√x-x^2) dx
    v = 149π/30

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