A Treatise on Infinitesimal Calculus ... |
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Page 25
... according as all the roots are unequal , or as some ( not all ) are equal to each other , we shall divide our inquiry into two parts . It will appear that the processes are equally applicable , whether the roots are real or impossible ...
... according as all the roots are unequal , or as some ( not all ) are equal to each other , we shall divide our inquiry into two parts . It will appear that the processes are equally applicable , whether the roots are real or impossible ...
Page 35
... 2π n 2π + - 1 sin n x 1 - is - 1 is ; 1 ( n n п { cos 2 + √1sin2 } ; is 1 ( { COS 2 = √1sin 2 " } ; п n n Combining the pairs of conjugate partial fractions according to equation F 2 23. ] 35 INTEGRATION OF RATIONAL FRACTIONS .
... 2π n 2π + - 1 sin n x 1 - is - 1 is ; 1 ( n n п { cos 2 + √1sin2 } ; is 1 ( { COS 2 = √1sin 2 " } ; п n n Combining the pairs of conjugate partial fractions according to equation F 2 23. ] 35 INTEGRATION OF RATIONAL FRACTIONS .
Page 39
... according to the process in- dicated in the preceding article . Again , let n be odd : then the roots of " +1 = 0 are π COS +1 sin COS + √ - 1 sin 3п n 3п n 2 n 2 COS n T√1 sin π , -1 ; n - 2 n so that if the conjugate partial ...
... according to the process in- dicated in the preceding article . Again , let n be odd : then the roots of " +1 = 0 are π COS +1 sin COS + √ - 1 sin 3п n 3п n 2 n 2 COS n T√1 sin π , -1 ; n - 2 n so that if the conjugate partial ...
Page 48
... according to - 1 Article 15 , and the result shewn to be equal to -tan - 1 X a dx 37. ] Integration of ( a + bx + cx2 ) b First let c be positive ; then , dx ( a + bx + cx2 ) = = + d ( x + 2/2 ) 612 1 { ( x log { x + 2 c 1 by reason of ...
... according to - 1 Article 15 , and the result shewn to be equal to -tan - 1 X a dx 37. ] Integration of ( a + bx + cx2 ) b First let c be positive ; then , dx ( a + bx + cx2 ) = = + d ( x + 2/2 ) 612 1 { ( x log { x + 2 c 1 by reason of ...
Page 73
... according to the form of n , the application of the method will be better exhibited by means of examples . Ex . 1. To integrate ( sin x ) dx . Employing the same abbreviation as in Art . 63 , Vol . I , let 21 sin = 2 -- -26 ( sinx ) ...
... according to the form of n , the application of the method will be better exhibited by means of examples . Ex . 1. To integrate ( sin x ) dx . Employing the same abbreviation as in Art . 63 , Vol . I , let 21 sin = 2 -- -26 ( sinx ) ...
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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