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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Cavalieri's quadrature formula ： ウィキペディア英語版 Cavalieri's quadrature formula In calculus, Cavalieri's quadrature formula, named for 17th-century Italian mathematician Bonaventura Cavalieri, is the integral :$\backslash int\_0^a\; x^n\backslash ,dx\; =\; \backslash tfrac\backslash ,\; a^\; \backslash qquad\; n\; \backslash geq\; 0,$ and generalizations thereof. This is the definite integral form; the indefinite integral form is: :$\backslash int\; x^n\backslash ,dx\; =\; \backslash tfrac\backslash ,\; x^\; +\; C\; \backslash qquad\; n\; \backslash neq\; -1.$ There are additional forms, listed below. Together with the linearity of the integral, this formula allows one to compute the integrals of all polynomials. The term "quadrature" is a traditional term for area; the integral is geometrically interpreted as the area under the curve ''y'' = ''x''''n''. Traditionally important cases are ''y'' = ''x''2, the quadrature of the parabola, known in antiquity, and ''y'' = 1/''x'', the quadrature of the hyperbola, whose value is a logarithm. == Forms == 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Cavalieri's quadrature formula」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.