Abstract
This chapter highlights a few geometrical applications of the definite integrals. It discusses the applications of calculus to curves rather than to applications from the physical world. The rigorous procedure by which Archimedes obtained the area of a parabolic segment is virtually integration, though this process is disguised by his techniques, the method of exhaustion. The chapter describes the area in polar coordinates, volume of a solid of revolution, length of a curve, and surface area of a solid revolution. It also highlights the volume and surface area of a solid of revolution.
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