Solid of revolutions divided into 10 cylindrical shells

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The equation f(x) = x^2 - x^3 reveals a complex relationship between variables that necessitates a rigorous approach to solve for the revolving shape about the y-axis. Created with the intention of acquainting students with the cylindrical shells method, this calculation provides an effective means of calculating volume when traditional methods fail. Although initial attempts may require adjustment, carefully dissecting the separation between cylindrical shells can lead to accurate results. Initially, my first effort resulted in failure to isolate distinct shells, emphasizing the importance of meticulous attention to detail and refinement of technique.