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Calculus

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The area is bounded by y= x^3, x= 2 is rotated around the x-axis. Find the volume using calculus.

  • Calculus - ,

    I will assume that the x-axis was the other boundary of the region we are rotating

    Using discs ...
    radius = y = x^3

    volume = π∫ y^2 dx from 0 to 2
    = π∫ x^6 dx from 0 to 2
    = π[ (1/7)x^7 ] from 0 to 2
    = π((1/7)(2^7) - 0 ]
    = 128π/7

  • Calculus - ,

    It is not clear to me how you would do this without using calculus :)

    Graph a sketch of it first. The corners are at (0,0) , (2,0) and (2,8)
    Lets add up a bunch of thin cylinders with axes along x axis
    volume of thin cylinder = pi y^2 dx
    so
    in from x = 0 to x = 2 of pi (x^3)^2 dx

    or pi x^6 dx

    or pi (1/7)x^7
    or 1/7 (128)
    about 18.3

  • times pi - ,

    I forgot to multiply by pi

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