A Treatise on Infinitesimal Calculus ... |
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Page 42
... preceding methods : but the process of integration by parts leads to a result more convenient , and better suited in most cases for finding the definite integral . Integration of dx ( x2 + a2 ) " In the formula , fudv = UV- let u = 42 ...
... preceding methods : but the process of integration by parts leads to a result more convenient , and better suited in most cases for finding the definite integral . Integration of dx ( x2 + a2 ) " In the formula , fudv = UV- let u = 42 ...
Page 65
... preceding are the integrals of the simpler exponential functions ; other combinations however often admit of reduction to algebraic forms by means of substitution , and thereby of inte- gration by the methods of the last Chapter ; of ...
... preceding are the integrals of the simpler exponential functions ; other combinations however often admit of reduction to algebraic forms by means of substitution , and thereby of inte- gration by the methods of the last Chapter ; of ...
Page 67
... preceding formulæ are of course 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 ) ...
... preceding formulæ are of course 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 ) ...
Page 91
... preceding have been investigated , because they will become hereafter the subject - matter for illustration of general theorems . SECTION 2. - The Change of Limits in Definite Integrals . - The Resolution of a Definite Integral into two ...
... preceding have been investigated , because they will become hereafter the subject - matter for illustration of general theorems . SECTION 2. - The Change of Limits in Definite Integrals . - The Resolution of a Definite Integral into two ...
Page 95
... preceding process depend . And the answer depends on the view taken of infinity . If infinity , which is the superior limit of the integral , is capable of discon- tinuous increase by units , the preceding process will probably be ...
... preceding process depend . And the answer depends on the view taken of infinity . If infinity , which is the superior limit of the integral , is capable of discon- tinuous increase by units , the preceding process will probably be ...
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A Treatise on Infinitesimal Calculus: Containing Differential and Integral ... Bartholomew Price No preview available - 2015 |
Common terms and phrases
a₁ angle application axis Beta-function bx dx consequently convergent convergent series coordinates cosec cx² cycloid definite integral denoted determined double integral dx a² dx dx dx dy dx² dy dz dy² dz dy dx e-ax element-function ellipse equal evaluation examples expressed fraction function Gamma-function geodesic geometrical given Hence infinite infinitesimal infinitesimal element Integral Calculus intrinsic equation length let us suppose limits of integration logr multiple integral plane curve preceding problem proper fraction quantity radius range of integration replaced result right-hand member subject-variable substituting surface symbols theorem tion values variables variation x-integration x₁ x2 dx x²)¹ x²)³