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Calculus

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Find the volume using the shell method - about the x-axis

x=y^2/3

  • Calculus -

    v = ∫2πrh dy
    where r=y and h=x
    v = 2π∫xy dy

    Can't tell whether you mean (y^2)/3 or y^(2/3)

    anyway, plug it in and use the appropriate limits.

  • Calculus -

    It is y^(2/3) - we have not gone over shell method yet so.....

  • Calculus -

    so, you have
    v = 2π∫(y^(2/3))y dy
    = 2π∫y^(5/3) dy
    = 2π (3/7) y^(7/3)

    but you need to specify the limits of integration, since the curve is open-ended.

    visit wolframalpha.com and enter

    plot y^2 = x^3

  • Calculus -

    The limits are 0,3

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