Calculus

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Construction of a solid of revolution of the area under a curve in shells.

Illustration showing the construction of a solid of revolution using the shell method. Displays the bounded region between two curves, the formation of cylindrical shells, and the final 3D solid generated by revolving the region around the axis y = −3.

This illustration presents the process of constructing a solid of revolution through the shell method, shown in three stages labeled (A), (B), and (C). The goal is to revolve a bounded area between two curves around a horizontal axis to generate a 3D solid.

This diagram serves as an educational tool for calculus and integral geometry, helping students understand how to compute the volume of solids using the shell method. It’s useful for scenarios where revolving a 2D region results in a 3D object with complex internal geometry.

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