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

### From inside the book

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**preceding article**let da √ - x √ ( 2αx — a2 ) dx dz - a be required . Assume x = thus 1 2 = ( 1-2 ) : and √ dx dx dz a2 ) dz α , - = x √ ( 2αx — a2 ) dz 1 x √ ( 2αx 1 dz - -va ===== 1 a √ { 2 ( 1. — z ) − ( 1 − 2 ) 2 } 1 -1 х α ... Page 40

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**preceding article**if we make a = c2 , b = −1 , n = 2 , p = xdx Another example is furnished by √ ( 2 ) be written xdx article we make b ― = - 2 . which may ; if in equation ( 4 ) of the preceding − 1 , n = 1 , p = - into 2a and m + ... Page 71

... called the rectification of the curve , because we may suppose the question to be this : Find a right line equal in length to any assigned portion of the curve . In the

... called the rectification of the curve , because we may suppose the question to be this : Find a right line equal in length to any assigned portion of the curve . In the

**preceding article**we have shewn that the length Lengths of Curves ΤΙ. Page 72

Isaac Todhunter. In the

Isaac Todhunter. In the

**preceding article**we have shewn that the length of an arc of a curve will be known if a ...**preceding article**we have found the value of the constant C , but in applying the formula to ascertain the lengths ... Page 75

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**preceding article**, ds аф = √ ( a2 cos2 + b2 sin2 4 ) , and s = √√ ( a2 4 + b2 = [ √ ( a2 cos2 6 + b2 sin2 p ) dô = a f√ ( 1 − e2 sin2 4 ) dp . - The exact integral cannot be obtained ; we may however expand √ ( 1 − e2 sin2 ) in ...### 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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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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