Cal 2

The region between the graphs of y=x^2 and y=3x is rotated around the line x=3. The volume of the resulting solid is

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  1. the curves intersect at (0,0) and (3,9). So,

    v = ∫[0,3] 2πrh dx
    where r=3-x and h=3x-x^2

    or,

    ∫[0,9] π(R^2-r^2) dy
    where R=(3-y/3) and r=(3-√y)

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  2. 1080pi

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