A Treatise on Infinitesimal Calculus ... |
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Page 3
... divided into n infinitesimal parts , and let x ,, x2 , .. x - 1 be the values of a corresponding to the points of partition . Let s be the definite integral ; then observing that f ( x ) is multiplied by the increment immediately ...
... divided into n infinitesimal parts , and let x ,, x2 , .. x - 1 be the values of a corresponding to the points of partition . Let s be the definite integral ; then observing that f ( x ) is multiplied by the increment immediately ...
Page 4
... divided into n equal infinitesimal parts , each of which = i ; so that Xnxo = ni ; i = Xn - n in the result , n = ∞ ; then the 4 [ 3 . THE DIFFERENTIAL CALCULUS The value of a surface-element in terms of the same, examples.
... divided into n equal infinitesimal parts , each of which = i ; so that Xnxo = ni ; i = Xn - n in the result , n = ∞ ; then the 4 [ 3 . THE DIFFERENTIAL CALCULUS The value of a surface-element in terms of the same, examples.
Page 6
... divided into n infinitesimal parts ; and let x1 , x2 , ... , _ , correspond to the ( n − 1 ) points of partition ; then by ( 1 ) , 2-1 S = f ( x ) ( x1 − x ̧ ) + ƒ ( X1 ) ( X2 − X1 ) + ... + ƒ ( xn − 1 ) ( xn− xn − 1 ) . ( 4 ) Now ...
... divided into n infinitesimal parts ; and let x1 , x2 , ... , _ , correspond to the ( n − 1 ) points of partition ; then by ( 1 ) , 2-1 S = f ( x ) ( x1 − x ̧ ) + ƒ ( X1 ) ( X2 − X1 ) + ... + ƒ ( xn − 1 ) ( xn− xn − 1 ) . ( 4 ) Now ...
Page 8
... divided into n parts , and $ 1 , 2 , 3 , E to be the values of a corresponding to the points of partition , and F ( x ) da to be the infinitesimal element : then the sum of all the infinitesimal elements corresponding to the successive ...
... divided into n parts , and $ 1 , 2 , 3 , E to be the values of a corresponding to the points of partition , and F ( x ) da to be the infinitesimal element : then the sum of all the infinitesimal elements corresponding to the successive ...
Page 13
... divided into n infinitesimal parts , and let x1 , x2 , ... , - be the values of a corresponding to the points of partition ; then dx = x1 - xo + X2 − X1 + X3 − X 2 + ... + X - X - 1 Ex . 2. To determine ΤΟ xa dx . be the values of a ...
... divided into n infinitesimal parts , and let x1 , x2 , ... , - be the values of a corresponding to the points of partition ; then dx = x1 - xo + X2 − X1 + X3 − X 2 + ... + X - X - 1 Ex . 2. To determine ΤΟ xa dx . be the values of a ...
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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