Rotating y = x² from 0 to 2 Around y-axis

Calculus 2 · Axiom Academy

EXAMPLE Rotating y = x^2 from 0 to 2 Around the y-axis Find the volume of the solid of revolution using the shell method The region under y = x^2 from x = 0 to x = 2 is revolved about the y-axis . Find the volume of the resulting solid. Nice work — you computed the volume with the shell method, step by step. Here is what to carry forward: Shell method advantage: rotating about the y-axis, the shell method uses x directly, so you never have to solve y = x^2 for . The formula: , where the radius is the distance from the axis and the height is the function value. Here: radius = x , height = x^2 , so . Choose your method wisely: the shell method shines exactly when it lets you avoid solving for the other variable.

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