A Treatise on Infinitesimal Calculus ... |
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Page 17
... true for x and simple functions of a , are also true for compound functions . SECTION I. - Integration of Fundamental Algebraical Functions . 11. ] Integration of x " dx . d.xm = mxm − 1 dx ; Since . ' . Imam - 1 da dx = x ; Xm dx ...
... true for x and simple functions of a , are also true for compound functions . SECTION I. - Integration of Fundamental Algebraical Functions . 11. ] Integration of x " dx . d.xm = mxm − 1 dx ; Since . ' . Imam - 1 da dx = x ; Xm dx ...
Page 18
... true for all integral and fractional , positive and negative , values of n , with the exception of , n = −1 ; in which case the right - hand member becomes ∞ , and the for- mula ceases to give an intelligible result : we must ...
... true for all integral and fractional , positive and negative , values of n , with the exception of , n = −1 ; in which case the right - hand member becomes ∞ , and the for- mula ceases to give an intelligible result : we must ...
Page 46
... true in the forms of indefinite integrals . 32. ] Integration of dx ( 2 ax — x2 ) - Since -1 d . versin x a = dx ( 2 ax - x2 ) dx x = versin -1 a Or thus , dx So ( 2 ax — x2 ) 1 = ( 2 ax - x2 ) -d ( a - x ) { a2 — ( a − x ) 2 } } 33 ...
... true in the forms of indefinite integrals . 32. ] Integration of dx ( 2 ax — x2 ) - Since -1 d . versin x a = dx ( 2 ax - x2 ) dx x = versin -1 a Or thus , dx So ( 2 ax — x2 ) 1 = ( 2 ax - x2 ) -d ( a - x ) { a2 — ( a − x ) 2 } } 33 ...
Page 67
... true when for x any function of x , say f ( x ) , is substituted , provided that do is replaced by f ' ( x ) dx . J sin ( mx + n ) dx 1 Thus = 1 m Jsin 1 m sin ( mx + n ) d ( mx + n ) cos ( mx + n ) . [ sin ( x3 ) x2 dx = { } [ sin ( x3 ) ...
... true when for x any function of x , say f ( x ) , is substituted , provided that do is replaced by f ' ( x ) dx . J sin ( mx + n ) dx 1 Thus = 1 m Jsin 1 m sin ( mx + n ) d ( mx + n ) cos ( mx + n ) . [ sin ( x3 ) x2 dx = { } [ sin ( x3 ) ...
Page 92
... true because they are true of ( 21 ) . This is the point of view from which definite integrals have been considered in Art . 8 , and from which they are always to be considered . Hence it is evident that if F ( x ) does not change sign ...
... true because they are true of ( 21 ) . This is the point of view from which definite integrals have been considered in Art . 8 , and from which they are always to be considered . Hence it is evident that if F ( x ) does not change sign ...
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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