Math

Find the volume of the solid obtained by rotating the region enclosed by y=x^2, y=6x about the line x=0using the method of disks or washers.

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  1. the curves intersect at (0,0) and (6,36)

    using washers of thickness dx, we have

    v = ∫[0,6] π(R^2-r^2) dx
    where R=6x and r=x^2
    v = ∫[0,6] π(36x^2-x^4) dx = 5184π/5

    To check, try using shells of thickness dy:

    v = ∫[0,36] 2πrh dy
    where r=y and h=√y-y/6
    v = ∫[0,36] 2πy(√y-y/6) dy = 5184π/5

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  2. How did u get all of that

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