## A treatise on the integral calculus and its applications1857 |

### From inside the book

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**tion**is the integral of a proposed function , we may if we please add to such integral any constant quantity . Integration then will for some time appear to be merely the inverse of differentiation , and we might have so defined it ; we ... Page 23

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**tion**of a of the ( n - 1 ) th degree . If we equate the coefficients of the different powers of x in this numerator with the cor- responding coefficients in U , we shall have n equations of the first degree to determine the n quantities ... Page 52

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**tion**to be integrated becomes infinite between the limits of integration , the rules of integration cannot be applied ; at least the case must be specially examined . ra dx Lov ; the value of this integral is 45. Consider ( 12 ) 0 2-2 ... Page 53

Isaac Todhunter.

Isaac Todhunter.

**tion**of the following statement : " “「 1- . is always finite if a be any quantity less than unity , and by taking a suffici- ently near to unity , we can make the value of the integral differ as little as we please from ... Page 56

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**tion**( 3 ) of Årt . 41 ; therefore therefore 0 : = · [ * " ( π2 – 2π0 ) log sin ✪ de , [ log sin π Ꮎ log sin Ꮎ d Ꮎ = log sin e de Required flog ( 1 + x ) 1 + x2 0 П 0 log 2 dx . Put x = tany , and the integral becomes [ * log ( 1 + ...### Other editions - View all

### Common terms and phrases

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

### Popular passages

Page 13 - Prize Essay for 1877. 8vo. 8.r. 6V. SMITH— Works by the Rev. BARNARD SMITH, MA, Rector of Glaston, Rutland, late Fellow and Senior Bursar of St. Peter's College, Cambridge. ARITHMETIC AND ALGEBRA, in their Principles and Application ; with numerous systematically arranged Examples taken from the Cambridge Examination Papers, with especial reference to the Ordinary Examination for the BA Degree.

Page 8 - Essays, Biographical and Critical; chiefly on the English PoetS. By DAVID MASSON, MA Professor of English Literature in University College, London.

Page 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.

Page 4 - Law," in which a comparison is occasionally made between the Roman Laws and those of England, by Samuel Hallifax, late Lord Bishop of St.

Page 15 - The fitness of Holy Scripture for Unfolding the Spiritual Life of Man : Christ the Desire of all Nations ; or, the Unconscious Prophecies of Heathendom.

Page 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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Page 4 - FROST.— The First Three Sections of Newton's Principia. With Notes and Problems in illustration of the subject. By PERCIVAL FROST, MA late Fellow of St. John's College, Cambridge, and Mathematical Lecturer of Jesus College. Crown 8vo. cloth, 10s.

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