A treatise on the integral calculus and its applications1857 |
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Página 2
... vanish . From these equations we have by addition ψ ( 6 ) - ψ ( α ) = Σφ ( α ) Δα + Σηρ . Now Σhp is less than ( ba ) p ' where p ' denotes the greatest of the quantities P1 , P2 , ... P ; hence Zho ultimately vanishes , and we obtain ...
... vanish . From these equations we have by addition ψ ( 6 ) - ψ ( α ) = Σφ ( α ) Δα + Σηρ . Now Σhp is less than ( ba ) p ' where p ' denotes the greatest of the quantities P1 , P2 , ... P ; hence Zho ultimately vanishes , and we obtain ...
Página 3
... vanishes . 6. The above process is called Integration ; the quantity f ( x ) dx is called a definite integral , and a and b are called a ф the limits of the integral . Since the value of this definite integral is ( b ) ( a ) we must ...
... vanishes . 6. The above process is called Integration ; the quantity f ( x ) dx is called a definite integral , and a and b are called a ф the limits of the integral . Since the value of this definite integral is ( b ) ( a ) we must ...
Página 24
... vanishes when x = a , and is there- fore divisible by x - a ; suppose the quotient denoted by x ( x ) , then $ ( x ) X ( x ) = F ( x ) ̄ ̄ ̄ ( x − a ) " ̄1 f ( x ) + $ ( a ) f ( a ) ( x − a ) ” ° 1 - The process may now be repeated on ...
... vanishes when x = a , and is there- fore divisible by x - a ; suppose the quotient denoted by x ( x ) , then $ ( x ) X ( x ) = F ( x ) ̄ ̄ ̄ ( x − a ) " ̄1 f ( x ) + $ ( a ) f ( a ) ( x − a ) ” ° 1 - The process may now be repeated on ...
Página 41
... 2 suppose positive quantity , then x ( c2x2 ) vanishes both when x = 0 and when x = c . Hence - [ ' * ( c2 — x2 ) * dx = nc2 n ( c2 n + 1 The following is a similar example . By integration by FORMULE OF REDUCTION . 41 Formulæ of Reduction.
... 2 suppose positive quantity , then x ( c2x2 ) vanishes both when x = 0 and when x = c . Hence - [ ' * ( c2 — x2 ) * dx = nc2 n ( c2 n + 1 The following is a similar example . By integration by FORMULE OF REDUCTION . 41 Formulæ of Reduction.
Página 67
... vanishes . Pr + 1 B Let ( * $ ( x , y ) dy be denoted by ✨ ( ~ , ) ; then add all the a horizontal rows and we obtain a result which we may de- note by Σh f ( x ) + Σhp . Now diminish indefinitely each term of which h is the 5-2 DOUBLE ...
... vanishes . Pr + 1 B Let ( * $ ( x , y ) dy be denoted by ✨ ( ~ , ) ; then add all the a horizontal rows and we obtain a result which we may de- note by Σh f ( x ) + Σhp . Now diminish indefinitely each term of which h is the 5-2 DOUBLE ...
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A Treatise on the Integral Calculus and Its Applications with Numerous Examples Isaac Todhunter Visualização integral - 1878 |
A Treatise on the Integral Calculus and Its Applications with Numerous Examples Isaac Todhunter Visualização integral - 1886 |
Palavras e frases frequentes
Application c² sin² Cambridge circle cloth co-ordinates constant cos² cos³ Crown 8vo curve cycloid definite integral denote differential coefficient double integral dx dx dx dy dz dy dx dz dx element ellipse equal Eulerian integral example expression Fcap Fellow of St Find the area find the volume formula function Hence indefinitely Integral Calculus integrate with respect intrinsic equation John's College latus rectum length limits M.A. Fellow MACMILLAN & CO.'S numerous obtain ordinate parabola partial fractions perpendicular plane positive preceding article radius vector result revolution revolve round round the axis shew sin² solid suppose surface tangent tion tractory transformed integral Trinity College unity vanishes variables vertex x₁ Y₁ πα аф
Passagens conhecidas
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Página 8 - Essays, Biographical and Critical; chiefly on the English PoetS. By DAVID MASSON, MA Professor of English Literature in University College, London.
Página 16 - THE SEVEN KINGS OF ROME. An Easy Narrative, abridged from the First Book of Livy by the omission of Difficult Passages; being a First Latin Reading Book, with Grammatical Notes and Vocabulary.
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Página 2 - The Evidences of Christianity as Exhibited in the Writings of its Apologists down to Augustine. An Essay which obtained the Hulsean Prize for the Year 1852. By WJ BOLTON, of Gonville and Caius College, Cambridge. 8vo. cloth, 6s.
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