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Calculus

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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=0, y=x(3-x) about the axis x = 0

  • Calculus - ,

    volume = π[integral]y^2 dx from x = 0 to x = 3

    y=x(3-x)
    y^2 = x^2(3-x)^2
    = x^2(9 - 6x + x^2)
    = 9x^2 - 6x^3 + x^4

    the integral of that is
    3x^3 - (3/2)x^4 + (1/5)x^5

    so volume
    = π(81 - 243/2 + 243/5 - 0)
    = (17/2)π

    check my arithmetic

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