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

### From inside the book

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**transformation**of multiple**integrals**is one of the most interesting parts of the subject , and the experience of teachers shews that the usual modes of treating it are not free from obscurity . I have therefore adopted a method ... Page 100

... ) - dy 2 + 2 + de de dz 2 and S = dr 2 = de . + 2 sin2 0 αφ ( dp ) 2 de . + x2 , dr \ 2 + + r2 sin2 0 ( do de de . de This may be

... ) - dy 2 + 2 + de de dz 2 and S = dr 2 = de . + 2 sin2 0 αφ ( dp ) 2 de . + x2 , dr \ 2 + + r2 sin2 0 ( do de de . de This may be

**transformed**into do 2 S = + 1 + r2 sin2 0 ' do dr dr dr or into 2 # = √ √ √ / { 100 LENGTHS OF CURVES . Page 133

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**integration**are 0 and a shall find a2 S = • sin a cos a · Hence we cos a 174. Instead of taking the element of the ...**transformed**into S = ] ] √ { r sin ' 0+ dr 2 de dr sin 0+ \ do :) " } rde do . An independent geometrical proof ... Page 181

... integration with respect to x is performed first , the limits will be x = 0 and x = √ ( ay ) , and then the limits for y will be y = 0 and y = a . Thus the

... integration with respect to x is performed first , the limits will be x = 0 and x = √ ( ay ) , and then the limits for y will be y = 0 and y = a . Thus the

**transformed integral**is faf √ia2 - 39 $ ( x , y ) dy dx . 231. Change the ... Page 182

Isaac Todhunter. Thus the

Isaac Todhunter. Thus the

**transformed integral**is go 2acos - 1 2a ¤ ( r , 0 ) r dr de . 0 0 232. Change the order of integration in Y 2a 3a - x papa- [ * [ ** ̄ * ‡ ( x , y ) dx dy . 4a B -X The integration for y is taken from y = x2 22 ...### 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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