A Treatise on Infinitesimal Calculus ... |
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Page xi
... investigate the con- ditions necessary for their application to other sub- ject - matter . Hence it is that the Definite Integrals of simple element - functions are investigated in the early part of the treatise from first principles ...
... investigate the con- ditions necessary for their application to other sub- ject - matter . Hence it is that the Definite Integrals of simple element - functions are investigated in the early part of the treatise from first principles ...
Page 53
... investigated in the first two sections of the present chapter ; the process of such transformation is called Rationalization , and we proceed to inquire into the condi- tions requisite for its application in certain cases . p To find ...
... investigated in the first two sections of the present chapter ; the process of such transformation is called Rationalization , and we proceed to inquire into the condi- tions requisite for its application in certain cases . p To find ...
Page 85
... investigate other theorems , and chiefly with the view to the evaluation of the integrals . Great care will be needed in the inquiry , as the subject is of a very delicate nature ; for a definite integral is the sum of a series , and ...
... investigate other theorems , and chiefly with the view to the evaluation of the integrals . Great care will be needed in the inquiry , as the subject is of a very delicate nature ; for a definite integral is the sum of a series , and ...
Page 91
... 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 or more connected ...
... 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 or more connected ...
Page 92
... investigate certain simple cases of a change of limits ; and in the first place the effect of a reversal of the limits . Xn By the definition of a definite integral , xo F ' ( x ) dx = ( xn− 1 − X „ ) F ′ ( X » ) + ( xn − 2 −X n ...
... investigate certain simple cases of a change of limits ; and in the first place the effect of a reversal of the limits . Xn By the definition of a definite integral , xo F ' ( x ) dx = ( xn− 1 − X „ ) F ′ ( X » ) + ( xn − 2 −X n ...
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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