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Revolution around the x-axis means that y forms the radius of revolution and dx is the thickness of the infinitesimal disc that has a volume πy2dx. When y=1, x=1, so x starts at 0 (the vertex of y=x4) and moves towards x=1, while radius y goes from 0 to 1. The integral is 01(πy2)dx=π01x8dx=π[x9/9]01=π/9 cubic units.

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