A Treatise on Infinitesimal Calculus ... |
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Page 128
... included in the definite integral ; so that all those lying beyond that limit , and up to infinity , may be included without change of value of the integral : in this case A = -1 / −1 [ * { ƒ ( f + i + y√ / −1 ) −ƒ ' ( E − i + y ...
... included in the definite integral ; so that all those lying beyond that limit , and up to infinity , may be included without change of value of the integral : in this case A = -1 / −1 [ * { ƒ ( f + i + y√ / −1 ) −ƒ ' ( E − i + y ...
Page 147
... included within the range of integration , 1 1 > > 1 ; ( 1 − x2 ) 3 ( 1 − x3 ) dx • } dx > ( 1 − x2 ) 3 - π 6 > ( 1 − x3 ) 3 S dx ; dx 1 0 ( 1 − ∞3 ) 2 .52358 > dx ( 1 - x3 ) > .5 ; ( 223 ) so that limits are assigned very near ...
... included within the range of integration , 1 1 > > 1 ; ( 1 − x2 ) 3 ( 1 − x3 ) dx • } dx > ( 1 − x2 ) 3 - π 6 > ( 1 − x3 ) 3 S dx ; dx 1 0 ( 1 − ∞3 ) 2 .52358 > dx ( 1 - x3 ) > .5 ; ( 223 ) so that limits are assigned very near ...
Page 178
... included within the range of integration , the results are doubtless correct . They may also be verified in the following way . Expanding cos bx we have e - axxn - 1 cos bx dx = e - ax 0 r ( n ) b2 г ( n + 2 ) = an 1.2 an + 2 + n ( n + ...
... included within the range of integration , the results are doubtless correct . They may also be verified in the following way . Expanding cos bx we have e - axxn - 1 cos bx dx = e - ax 0 r ( n ) b2 г ( n + 2 ) = an 1.2 an + 2 + n ( n + ...
Page 255
... included in the definite integral . x 1 Again , in ( 55 ) , let ≈ = 2 ; then T = 116 12 1 1 + 1.3 1 2 3 ( 2 ) 3 + + 2.4 5 ( 2 ) 5 1.3.5 1 2.4.6 7 ( 2 ) 7 + .... ( 57 ) -1 Also , since sin1x + cos ̄1x = П cos 194. ] 255 BY INTEGRATION .
... included in the definite integral . x 1 Again , in ( 55 ) , let ≈ = 2 ; then T = 116 12 1 1 + 1.3 1 2 3 ( 2 ) 3 + + 2.4 5 ( 2 ) 5 1.3.5 1 2.4.6 7 ( 2 ) 7 + .... ( 57 ) -1 Also , since sin1x + cos ̄1x = П cos 194. ] 255 BY INTEGRATION .
Page 263
... included which are not within the range of integration ; and consequently the limits of § in the § - integration are 0 and -i ; and the value of the definite integral in the right - hand member of ( 82 ) is , the limits being 0 and ...
... included which are not within the range of integration ; and consequently the limits of § in the § - integration are 0 and -i ; and the value of the definite integral in the right - hand member of ( 82 ) is , the limits being 0 and ...
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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