A Treatise on Infinitesimal Calculus ... |
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Page 67
... ( cosec mx ) 2 dx ; dx ( sin mx ) 2 dx ( cosec x ) 3 dx = √ ( sin x ) 2 ( 12 ) ( 13 ) J cot mx ; ( 14 ) m - cot x . ( 15 ) Similarly , Jse 1 sec mx tan mx dx = sec mx ; ( 16 ) m 1 cosec mx . ( 17 ) m Scosec cosec mx cot mx dx = 66. ] And ...
... ( cosec mx ) 2 dx ; dx ( sin mx ) 2 dx ( cosec x ) 3 dx = √ ( sin x ) 2 ( 12 ) ( 13 ) J cot mx ; ( 14 ) m - cot x . ( 15 ) Similarly , Jse 1 sec mx tan mx dx = sec mx ; ( 16 ) m 1 cosec mx . ( 17 ) m Scosec cosec mx cot mx dx = 66. ] And ...
Page 68
... dx = f { ( sec x ) 3 — 1 } dr = tan x - X . f ( cot x ) 3 dx = [ { ( cosec x ) 3 — 1 } dx 82812 ( 18 ) ( 19 ) ( 20 ) ( 21 ) ( 22 ) ( 23 ) ( 24 ) = - cot x - x . ( 25 ) dx 1 + b cos x = = f · 68 [ 67 . INTEGRATION OF CIRCULAR FUNCTIONS .
... dx = f { ( sec x ) 3 — 1 } dr = tan x - X . f ( cot x ) 3 dx = [ { ( cosec x ) 3 — 1 } dx 82812 ( 18 ) ( 19 ) ( 20 ) ( 21 ) ( 22 ) ( 23 ) ( 24 ) = - cot x - x . ( 25 ) dx 1 + b cos x = = f · 68 [ 67 . INTEGRATION OF CIRCULAR FUNCTIONS .
Page 74
... ( cosec x ) 2m dx m - 1 = √ { 1+ ( cot x ) 2 } TM −1 ( cosec a ) 2 dr = − √ { 1 + ( m −1 ) ( cot x ) 2 + = - / { = = { cot a = { cot cot x + ( m - 1 ) ( m −1 ) ( m — 2 ) 1.2 ( cot x ) a + } d.cotx ( cotz ) 3 + + 3 1.2 5 } . ( 41 ) ...
... ( cosec x ) 2m dx m - 1 = √ { 1+ ( cot x ) 2 } TM −1 ( cosec a ) 2 dr = − √ { 1 + ( m −1 ) ( cot x ) 2 + = - / { = = { cot a = { cot cot x + ( m - 1 ) ( m −1 ) ( m — 2 ) 1.2 ( cot x ) a + } d.cotx ( cotz ) 3 + + 3 1.2 5 } . ( 41 ) ...
Page 91
... cosec - π n 2m + 1 it may be shewn that π . 2n ( 17 ) process { 2m + 1 2m + 1 sin + sin 2 n n 2m + 1 + sin ( n - 1 ) n T } ( 18 ) П - • cot n 2m + 1 2n π . ( 19 ) As very many instances of the evaluation of a definite integral by means ...
... cosec - π n 2m + 1 it may be shewn that π . 2n ( 17 ) process { 2m + 1 2m + 1 sin + sin 2 n n 2m + 1 + sin ( n - 1 ) n T } ( 18 ) П - • cot n 2m + 1 2n π . ( 19 ) As very many instances of the evaluation of a definite integral by means ...
Page 102
... ( cosec x ) 2 − 1 } dæ = cot x - x ; - ( 54 ) that is , the sum of a series of positive quantities is a negative quantity which it of course cannot be . The preceding theory removes the apparent contradiction . Let the limits , whatever ...
... ( cosec x ) 2 − 1 } dæ = cot x - x ; - ( 54 ) that is , the sum of a series of positive quantities is a negative quantity which it of course cannot be . The preceding theory removes the apparent contradiction . Let the limits , whatever ...
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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