A Treatise on Infinitesimal Calculus ... |
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Results 6-10 of 59
Page 49
... employ the method of inte- gration by parts given by the formula , Judv dv = uv To determine f ( a2 — x2 ) 1 dx . Let u = ( a2 — x2 ) , --- -xdx – Svdu . dvdx ; ( 78 ) ... du = ( a2 — x2 ) PRICE , VOL . II . v = x . H Substituting which ...
... employ the method of inte- gration by parts given by the formula , Judv dv = uv To determine f ( a2 — x2 ) 1 dx . Let u = ( a2 — x2 ) , --- -xdx – Svdu . dvdx ; ( 78 ) ... du = ( a2 — x2 ) PRICE , VOL . II . v = x . H Substituting which ...
Page 73
... Employing the same abbreviation as in Art . 63 , Vol . I , let 21 sin x = 2 - 1 .. _2® ( sin ) ® = z® – 62 * + 1522_20 + 15 6 1 - + 1 ( sin x ) 6 = -―― 22 24 26 = 2 cos 6x - 12 cos 4x + 30 cos 2 x - 20 ; { cos 6x - 6 cos 4x + 15 cos 2 x ...
... Employing the same abbreviation as in Art . 63 , Vol . I , let 21 sin x = 2 - 1 .. _2® ( sin ) ® = z® – 62 * + 1522_20 + 15 6 1 - + 1 ( sin x ) 6 = -―― 22 24 26 = 2 cos 6x - 12 cos 4x + 30 cos 2 x - 20 ; { cos 6x - 6 cos 4x + 15 cos 2 x ...
Page 92
... employed values of its subject - variable . Now whenever a definite integral or its properties are the subjects of inquiry , the definite integral must be considered as the sum of the series given in ( 21 ) , and its theorems are true ...
... employed values of its subject - variable . Now whenever a definite integral or its properties are the subjects of inquiry , the definite integral must be considered as the sum of the series given in ( 21 ) , and its theorems are true ...
Page 98
... employed values of its subject- variable ; and our inquiry has been restricted to cases wherein this condition is fulfilled . Suppose however έ to be a value of x , within the range of integration , for which F ' ( x ) becomes either ...
... employed values of its subject- variable ; and our inquiry has been restricted to cases wherein this condition is fulfilled . Suppose however έ to be a value of x , within the range of integration , for which F ' ( x ) becomes either ...
Page 107
... employed values of its subject - variable . Ex . 1 . [ ® ƒ ( x " + x ̄ " ) logæ ! dx dx dx = [ ' f ( x * + x = " ) logæ + [ " f ( x + x ) log ad X In the second integral of the right - hand member for a sub- stitute 1 ; then dx dx ...
... employed values of its subject - variable . Ex . 1 . [ ® ƒ ( x " + x ̄ " ) logæ ! dx dx dx = [ ' f ( x * + x = " ) logæ + [ " f ( x + x ) log ad X In the second integral of the right - hand member for a sub- stitute 1 ; then dx dx ...
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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