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

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**Plane**Curves and of Surfaces VIII . Volumes of Solids IX . Differentiation of an Integral with respect to any quantity PAGE I 22 38 48 64 ΤΙ 103 142 which it may involve 165 X. Elliptic Integrals 174 XI . Change of the Variables in a ... Page 70

... and 7 , and 7 , may be functions of x . This triple integral is the limit of a certain series which may be denoted by Zo ( x , y , z ) Ax △ y Az . no 71 CHAPTER VI . LENGTHS OF CURVES .

... and 7 , and 7 , may be functions of x . This triple integral is the limit of a certain series which may be denoted by Zo ( x , y , z ) Ax △ y Az . no 71 CHAPTER VI . LENGTHS OF CURVES .

**Plane**Curves 70 DOUBLE INTEGRATION . Page 71

Isaac Todhunter. 71 CHAPTER VI . LENGTHS OF CURVES .

Isaac Todhunter. 71 CHAPTER VI . LENGTHS OF CURVES .

**Plane**Curves . Rectangular co - ordinates . 68. Let P be any point on the curve APQ , and let x , y be its co - ordinates ; let s denote the length of the arc AP measured from a fixed ... Page 75

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**Plane**Co - ordinate Geo- metry , Art . 168 ) . Therefore , by the 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 ... Page 76

Isaac Todhunter.

Isaac Todhunter.

**Plane**Curves . Polar Co - ordinates . 79. Let r , be the polar co - ordinates of any point of a curve , and s the length of the arc measured from any fixed point up to this point ; then ( Dif . Cal . Art . 311 ) hence ds ...### 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

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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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