## 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.

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