A Treatise on Infinitesimal Calculus ... |
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Page 22
... give the same result ; for suppose the limits to be x and xo ; then either form gives 1 2 a log ( xn + a ) ( x。− a ) ( x - a ) ( x + a ) , and the results are identical . In the exact process of definite integration then the apparent ...
... give the same result ; for suppose the limits to be x and xo ; then either form gives 1 2 a log ( xn + a ) ( x。− a ) ( x - a ) ( x + a ) , and the results are identical . In the exact process of definite integration then the apparent ...
Page 38
... - 1 sin n π n π π COS -V - 1 sin n n - - ( π COS + √ - 1 sin X- COS √1 sin n π - n π 2 x cos 2 which becomes - 1 n x2- 2 x cos n FIS π +1 and the other pairs give similar results ; so that 38 [ 24 . INTEGRATION OF RATIONAL FRACTIONS .
... - 1 sin n π n π π COS -V - 1 sin n n - - ( π COS + √ - 1 sin X- COS √1 sin n π - n π 2 x cos 2 which becomes - 1 n x2- 2 x cos n FIS π +1 and the other pairs give similar results ; so that 38 [ 24 . INTEGRATION OF RATIONAL FRACTIONS .
Page 39
Bartholomew Price. and the other pairs give similar results ; so that dr +1 dx x 3п - ( 2x cos - 2 ) dr 1 ( 2rcos - 2 ) dr n - n 3п x2 - 2x cos +1 π x2 - 2x cos +1 n n - 1 2x cos π - n N- -1 x2 - 2x cos n n 2 ) dx • ; ( 53 ) each of ...
Bartholomew Price. and the other pairs give similar results ; so that dr +1 dx x 3п - ( 2x cos - 2 ) dr 1 ( 2rcos - 2 ) dr n - n 3п x2 - 2x cos +1 π x2 - 2x cos +1 n n - 1 2x cos π - n N- -1 x2 - 2x cos n n 2 ) dx • ; ( 53 ) each of ...
Page 43
... give a determinate result : but the integral becomes and we have , see Art . 14 , dx + a2 , dx x2 1 X x2 + a2 a = - -1 tan α • ( 56 ) The method is known by the name of Integration by Successive Reduction . Ex . 1. Integration of dx x ...
... give a determinate result : but the integral becomes and we have , see Art . 14 , dx + a2 , dx x2 1 X x2 + a2 a = - -1 tan α • ( 56 ) The method is known by the name of Integration by Successive Reduction . Ex . 1. Integration of dx x ...
Page 44
... gives the following formula , dx = Ꮖ 1 2n - 3 + dx a2 - x2 ) n 2 ( n - 1 ) a2 ( a2 - x2 ) n - 1 a2 2n — 2. ( a2 — x2 ) " — 1 and by successive reduction the last integral becomes dx 1 = log a + x a2 x2 2a α - x -- the formula failing to ...
... gives the following formula , dx = Ꮖ 1 2n - 3 + dx a2 - x2 ) n 2 ( n - 1 ) a2 ( a2 - x2 ) n - 1 a2 2n — 2. ( a2 — x2 ) " — 1 and by successive reduction the last integral becomes dx 1 = log a + x a2 x2 2a α - x -- the formula failing to ...
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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