Volume of Rotation with Shell Method: Two Curves

This example demonstrates the volume of a solid of revolution formed by rotating the region between two curves, using the shell method (cylindrical shells). It highlights how the total volume can be assembled from infinitesimal shell contributions, emphasizing the geometric meaning of the definite integral. The core ideas include solids of revolution, the shell method, integration bounds determined by special points (notably the intersection of the two curves), and the role of symmetry in simplifying the construction. In GeoGebra, the rotation surface is created with the Surface command, while the underlying curves and key geometric/measurement objects (e.g., a, l1, b, d, f, e, g, dd, h, c, i) are used to define radii, heights, and the relevant interval structure. Suitable for high school to early college calculus instruction and for conceptual practice with volume-from-geometry problems.