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

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... 212 XIII . Expansion of

**Functions**in Trigonometrical Series 250 XIV . Application of the Integral Calculus to Questions of Mean Value and Probability 262 INTEGRAL CALCULUS . CHAPTER I. MEANING OF INTEGRATION . EXAMPLES. Page 1

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**function**a second**function**called the differential coefficient of the former ; in the Integral Calculus we have to return from the differential coefficient to the**function**from which it was deduced . We do not say that this is the ... Page 2

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**function**of x that ( x ) is the differential coefficient of it with respect to x . Then we know that the ( x + h ) — 4 ( x ) limit of h - ( x ) . Hence we may put where P1 , P2 , when h is indefinitely diminished is ↓ ( x1 ) — ( a ) ... Page 3

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**function**( x ) is to be integrated between assigned limits , first ascertain the**function**( x ) of which ( x ) is the differential coefficient . To express the connexion between ( x ) and ( x ) we have $ ( x ) = dy ( x ) dx " and this ... Page 4

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**function**from which ( x ) springs by differentiation , we denote this by the equation [ $ ( x ) dx = „ ( x ) , and we now proceed to methods of finding ( x ) when ( x ) is given . We have shewn , Dif . Cal . 4 APPLICATION OF INTEGRATION .### 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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