A Treatise on Infinitesimal Calculus ... |
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Page xxiii
... formula for transformation 284 286 287 214. Mode of assigning the new limits in the transformed in- tegral .. 290 215. Examples of transformation of definite multiple integrals 216. Cases in which the limits of the transformed integral ...
... formula for transformation 284 286 287 214. Mode of assigning the new limits in the transformed in- tegral .. 290 215. Examples of transformation of definite multiple integrals 216. Cases in which the limits of the transformed integral ...
Page xxv
... formula for the transformation of a double integral 250. More general forms of curvilinear coordinates .. CHAP . X. CUBATURE OF SOLIDS , SECTION 1. - Cubature of Solids of Revolution . 251. Investigation of the volume - element , when ...
... formula for the transformation of a double integral 250. More general forms of curvilinear coordinates .. CHAP . X. CUBATURE OF SOLIDS , SECTION 1. - Cubature of Solids of Revolution . 251. Investigation of the volume - element , when ...
Page 17
... formula of integration which are true for x and simple functions of a , are also true for compound functions . SECTION I. - Integration of Fundamental Algebraical Functions . 11. ] Integration of x " dx . d.xm = mxm − 1 dx ; Since ...
... formula of integration which are true for x and simple functions of a , are also true for compound functions . SECTION I. - Integration of Fundamental Algebraical Functions . 11. ] Integration of x " dx . d.xm = mxm − 1 dx ; Since ...
Page 18
... formula ( 7 ) is true for all integral and fractional , positive and negative , values of n , with the exception of , n = −1 ; in which case the right - hand member becomes ∞ , and the for- mula ceases to give an intelligible result ...
... formula ( 7 ) is true for all integral and fractional , positive and negative , values of n , with the exception of , n = −1 ; in which case the right - hand member becomes ∞ , and the for- mula ceases to give an intelligible result ...
Page 24
... formula of reduction . 18. ] A rational fraction is of the form Loxm - 2-1 - I1xm − 1 + Q 2 xm n - 1 x ” —P1x1 − 1 + ...... ± Im_1 x + Im Pn - 1x + Pn ( 19 ) the numerator and denominator being algebraical expressions involving only ...
... formula of reduction . 18. ] A rational fraction is of the form Loxm - 2-1 - I1xm − 1 + Q 2 xm n - 1 x ” —P1x1 − 1 + ...... ± Im_1 x + Im Pn - 1x + Pn ( 19 ) the numerator and denominator being algebraical expressions involving only ...
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A Treatise On Infinitesimal Calculus: Containing Differential and Integral ... Bartholomew Price No preview available - 2018 |
Common terms and phrases
a₁ angle application axis Beta-function bx dx consequently convergent convergent series coordinates cosec cx² cycloid definite integral denoted determined double integral dx a² dx dx dx dy dx² dy dz dy² dz dy dx e-ax element-function ellipse equal evaluation examples expressed fraction function Gamma-function geodesic geometrical given Hence infinite infinitesimal infinitesimal element Integral Calculus intrinsic equation length let us suppose limits of integration logr multiple integral plane curve preceding problem proper fraction quantity radius range of integration replaced result right-hand member subject-variable substituting surface symbols theorem tion values variables variation x-integration x₁ x2 dx x²)¹ x²)³