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

### From inside the book

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Page 125

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**round the axis**of x , and let S denote the area of the surface formed by the revolu- tion of AP ; then ( Dif . Cal . Art . 315 ) ds = 2πу ; ds S = √2wy ds therefore thus 8 = √2 and S ds S = 2πу dx ds dx ...... 8 = √2 wy do dy dy ... Page 126

... axis of x to revolve

... axis of x to revolve

**round the axis**of x , thus generating a right circular cylinder : let a be the distance of the revolving line from the axis of x ; then ds y = a , and = dx thus by equation ( 2 ) of Art . 161 , 1 ; S = 2π пра dx ... Page 127

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**round the axis**of x ; here dy dx == x y ds and = dx + dy 2 dx a = + y2 = y Hence by equation ( 2 ) of Art . 161 , α ... axis perpendicular to the planes and circumscribing the sphere . 165. Application to the Prolate Spheroid . Let ... Page 128

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**round the axis**of x . Let s , and s , denote the lengths of arcs measured from fixed points in the two curves up to the point whose abscissa is x . Let S denote the sum of the areas of both surfaces intercepted between two planes ... Page 140

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**round the axis**of x of the curve xy = k3 . XC 45. Also of the curve y = ae * • 46. Also of the catenary y = ¦ ( e2 + e ̄3 ) . 47. Shew that the whole surface of an oblate spheroid is 2πα { 1 - e2 1 + e + log 2e 1 - e 48. A cycloid revolves ...### 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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