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Unformatted text preview: More on Tabular Integration by Parts Leonard Gillman, The High Road, Austin, TX 78746 The College Mathematics Journal, November 1991, Volume 22, Number 5, pp. 407–410. This note comments on the engaging article by David Horowitz on “Tabular Integration by Parts” [ College Mathematics Journal 21 (1990) 307–311]. The method is based on iterating the diagram and can be ended at any stage. Table 1 shows how the procedure handles the integral A preliminary column lists alternating plus and minus signs, starting with plus. The integrand is written as a product of two factors, which head columns 1 and 2. Column 1 lists successive derivatives of the head entry, and column 2 successive antiderivatives of its head entry. The value of the integral is the sum of the indicated diagonal products, plus the integral of the product along the last row, all taken with the indicated signs. Note that if you reach a 0 in Column 1, as in the illustration, then the integral across that row provides the constant of integration. Table 1 As Horowitz shows, the method is a blockbuster, as can be seen from the way it knocks off an integral like not to mention Taylor’s formula and the other examples he presents....
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This note was uploaded on 07/11/2011 for the course MAC 2312 taught by Professor Bonner during the Spring '08 term at University of Florida.
- Spring '08
- Integration By Parts