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Re:[obm-l] substituicao de weirstrass

To: "obm-l" <obm-l@xxxxxxxxxxxxxx>
Subject: Re:[obm-l] substituicao de weirstrass
From: "ronaldo.luiz.alonso" <ronaldo.luiz.alonso@xxxxxxxxxx>
Date: Fri, 20 May 2005 13:13:30 -0300
Reply-To: obm-l@xxxxxxxxxxxxxx
Sender: owner-obm-l@xxxxxxxxxxxxxx

> Boa noite,

> Como posso calcular a integral de (3 + cost)^1/2 por substituicao de Weirstrass?

Bem. Inicialmente vamos esclarecer 'a

lista o que é a substituição de Weirstrass:

" The tan(x/2) substitution, also called the Weierstrass substitution, is one method currently used by computer-algebra systems for the evaluation of trigonometric integrals. The method needs to be improved, because the expressions obtained using it sometimes contain discontinuities, which unnecessarily limit the domains over which the expressions are correct. We show that the discontinuities are spurious in the following sense: Given an integrand and an expression for its antiderivative that was obtained by the Weierstrass substition, a better expression can be found that is continuous on wider intervals than the first expression and yet is still an antiderivative of the integrand. "

Referência: The evaluation of trigonometric integrals avoiding spurious discontinuitiesThe evaluation of trigonometric integrals avoiding spurious discontinuities ACM transactions on Mathematical Software (TOMS) Volume 20 , Issue 1 (March 1994) Pages: 124 - 135

> Desde já agradeco

> []s

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