A Treatise on Infinitesimal Calculus ... |
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Page xxii
... greater than unity 240 5 . 182. Σaƒ ( x ) is convergent or divergent according as [ ƒ ( x ) dx is finite or infinite .. 241 244 183. Examples of the criterion given in the preceding article 243 184. On comparable and incomparable series ...
... greater than unity 240 5 . 182. Σaƒ ( x ) is convergent or divergent according as [ ƒ ( x ) dx is finite or infinite .. 241 244 183. Examples of the criterion given in the preceding article 243 184. On comparable and incomparable series ...
Page 24
... being algebraical expressions involving only positive and integral powers of a , and 40 , 41 , ... Im P1 , P2 P being constants . ... When m is greater than , or equal to n 24 INTEGRATION OF RATIONAL FRACTIONS . [ 18 .
... being algebraical expressions involving only positive and integral powers of a , and 40 , 41 , ... Im P1 , P2 P being constants . ... When m is greater than , or equal to n 24 INTEGRATION OF RATIONAL FRACTIONS . [ 18 .
Page 25
Bartholomew Price. When m is greater than , or equal to n , ( 19 ) may by common division be reduced to the sum of an integral algebraical ex- pression , and of a fraction whose denominator will be the same as that of ( 19 ) , and whose ...
Bartholomew Price. When m is greater than , or equal to n , ( 19 ) may by common division be reduced to the sum of an integral algebraical ex- pression , and of a fraction whose denominator will be the same as that of ( 19 ) , and whose ...
Page 69
... greater than b ; then the last expression becomes dr a + b cos x = 2 a- a + b α b - X d.tan 2 ( 26 ) + ( tan ) 2 = tan - 1 tan • ( 27 ) a + ( a2 - b2 ) + ( 8 ) let a be less than b , then ( 26 ) becomes dx La + b cos x dx a + b sin ...
... greater than b ; then the last expression becomes dr a + b cos x = 2 a- a + b α b - X d.tan 2 ( 26 ) + ( tan ) 2 = tan - 1 tan • ( 27 ) a + ( a2 - b2 ) + ( 8 ) let a be less than b , then ( 26 ) becomes dx La + b cos x dx a + b sin ...
Page 81
... greater facility ; and by a reverse process many of the circular functions which have been integrated in the present Chapter may be transformed into algebraical functions . The method is exhibited by the following examples : Ex . 1. Ja ...
... greater facility ; and by a reverse process many of the circular functions which have been integrated in the present Chapter may be transformed into algebraical functions . The method is exhibited by the following examples : Ex . 1. Ja ...
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A Treatise on Infinitesimal Calculus: Containing Differential and Integral ... Bartholomew Price No preview available - 2015 |
Common terms and phrases
a₁ a₂ angle application axis Beta-function bx dx consequently convergent series coordinates cosec cx² cycloid definite integral denoted determined differential double integral dx a² dx dx dx dy dx Ex dx² dy dx dy² e-ax element-function ellipse equal evaluation expressed find the area finite and continuous fraction function Gamma-function geometrical given Hence infinite infinitesimal infinitesimal element Integral Calculus intrinsic equation involute left-hand member length let us suppose limits of integration multiple integrals plane curve polar coordinates preceding proper fraction radius range of integration replaced result right-hand member subject-variable substituting surface symbols theorem tion values variable x-integration x₁ x²)¹ x²)³ αξ πα