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

### From inside the book

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Page 72

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**latus rectum**x = = a ; hence the length of the arc between the vertex and one extremity of the**latus rectum**is a√2 + a log ( 1 + √√ / 2 ) . 71. In the preceding article we have found the value of the constant C , but in applying the ... Page 110

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**latus rectum**of the parabola , and therefore 2a the radius of the circle , the equation to the para- bola is y2 = 4a ( a − x ) , and that to the circle y2 = 4a2 — x2 . Suppose we integrate with respect to x first , then where 1 area ... Page 160

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**latus rectum**of the paraboloid being all equal . 11. Determine the volume of the solid generated by the re- volution of the curve ( x2 + y2 ) = ax + by about the axis of y , supposing a greater than b . Shew what the result becomes when ... Page 182

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**latus rectum**of the parabola . Thus the integration may be considered as extending over the area OLBSO . Now let the order of integration be changed ; we shall have to consider separately the spaces OLS and BLS . For the space OLS we ... Page 210

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**latus rectum**by dividing the area by a series of parabolas which touch these tangents and by a series of lines drawn from the intersection of the tangents . 14. Transform the triple integral [ ƒƒ.ƒ ( x , y , z ) dę dy dz into one 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

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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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