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Calculus 1 Help

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Find the volume generated by rotating about the given line

a) y^2=x, x=2y; about the y-axis

b) y=x, y=sqrtx; about y=1

  • Calculus 1 Help -

    (a)
    using shells of thickness dx,
    v = ∫[0,4] 2πrh dx
    where r=x and h=√x-x/2
    v = ∫[0,4] 2πx(√x-x/2) dx = 64π/15

    using discs of thickness dy,
    v = ∫[0,2] π(R^2-r^2) dy
    where R=2y and r=y^2
    v = ∫[0,2] π((2y)^2-y^4) dy = 64π/15

    Now you try (b), recalling the formulas for volumes of discs and shells, above. Sketch the curves and figure out the radius or height.

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