We now begin a study of the second principal concept of the calculus: integration. Its origins go back to Archimedes, who thought of areas (and volumes) as being made up of tiny pieces, each of which was a triangle or square or other regular figure. This is just the way you would think about the area of a tiled patio with a curved boundary. Since you know the area of each square tile, you need only count the tiles in order to obtain an approximate area for the whole patio. Archimedes then thought of the leftover regions of irregular shape at the edges as being filled in with smaller tiles, which gave a better fit. His method was to improve these approximations by a limiting process.
KeywordsTruncation Error Fundamental Theorem Decimal Place Definite Integral Correct Area
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