A Treatise on Infinitesimal Calculus ... |
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Page 6
... or D expresses the differential or infinitesimal element of a variable or of a function ; so we employ ( a long 8 ) to denote the general sum of an infinite number of terms , each of 6 THE SYMBOLS OF THE INTEGRAL CALCULus . [ 4 .
... or D expresses the differential or infinitesimal element of a variable or of a function ; so we employ ( a long 8 ) to denote the general sum of an infinite number of terms , each of 6 THE SYMBOLS OF THE INTEGRAL CALCULus . [ 4 .
Page 96
... denoted by [ * r ′ ( x ) da and F ( x ) dx , will consist of terms which are , term by term , equal to each other ; and consequently ' હૃ [ * r ' ′ ( x ) dx = [ * r ' ( x ) dx . xo In * } Hence [ ** ¥ ' ( x ) dx = [ ' * r ( * ¥ ' ( x ) ...
... denoted by [ * r ′ ( x ) da and F ( x ) dx , will consist of terms which are , term by term , equal to each other ; and consequently ' હૃ [ * r ' ′ ( x ) dx = [ * r ' ( x ) dx . xo In * } Hence [ ** ¥ ' ( x ) dx = [ ' * r ( * ¥ ' ( x ) ...
Page 97
... denoted by * r ′ ( x ) dæ and [ ** r ' ( x ) da , will consist of ξ terms which are , term by term , equal to each other , and of con- trary signs ; and consequently [ * x ( c ) dr = - [ " v ( x ) dx ; dx so that the sum of the two ...
... denoted by * r ′ ( x ) dæ and [ ** r ' ( x ) da , will consist of ξ terms which are , term by term , equal to each other , and of con- trary signs ; and consequently [ * x ( c ) dr = - [ " v ( x ) dx ; dx so that the sum of the two ...
Page 107
... denoted by ƒ in the following examples is finite and continuous for all 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 ...
... denoted by ƒ in the following examples is finite and continuous for all 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 ...
Page 125
... denote it by r ( m ) ; so that xm - le- * dx = г ( m ) ; Also let a = k cos a , b = k sin a ; then ( 136 ) becomes ( 137 ) cos ma - N - √1 sin ma ' r ( m ) ; ( 138 ) ( a2 + b2 ) xm - le - ax ( cos bx - 1 sin bx ) dx and equating ...
... denote it by r ( m ) ; so that xm - le- * dx = г ( m ) ; Also let a = k cos a , b = k sin a ; then ( 136 ) becomes ( 137 ) cos ma - N - √1 sin ma ' r ( m ) ; ( 138 ) ( a2 + b2 ) xm - le - ax ( cos bx - 1 sin bx ) dx and equating ...
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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