Ap calc

Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis.
x + y = 3, x = 4 − (y − 1)^2

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  1. the curves intersect at y=0,3 so the volume is

    v = ∫ 2πrh dy
    where r=y and h=4-(y-1)^2 - (3-y)
    v = ∫[0,3] 2πy(4-(y-1)^2 - (3-y)) dy = 27π/2

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  2. yoop

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  3. Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis.
    x = 30y2 − 6y3, x = 0

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