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Consider the solid obtained by rotating the region bounded by the given curves about the x-axis.

y = 6 x^6 , y = 6 x , x >= 0

Find the volume V of this solid.

  • calculus -

    The curves intersect at x = 0 and x = 1. The region bounded between those curves has y-separation of 6(x-x^6).
    For the total enclosed area, integrate that function times dx from x=0 to x=1.

  • calculus (correction) -

    I forgot that you wanted the volume of the solid obtained by rotating the curves about the x axis. This changes the formula to

    Integral of 36 pi (x^2 - x^12) dx
    ...0 to 1

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