A Treatise on Infinitesimal Calculus ... |
From inside the book
Results 1-5 of 45
Page xx
... negative SECTION 8. - The Logarithm - Integral . 147. Definition of the logarithm - integral , and its expansion 148. Various applications of the logarithm - integral . 187 .. 189 CHAP . V. SUCCESSIVE INTEGRATION OF AN EXPLICIT FUNCTION ...
... negative SECTION 8. - The Logarithm - Integral . 147. Definition of the logarithm - integral , and its expansion 148. Various applications of the logarithm - integral . 187 .. 189 CHAP . V. SUCCESSIVE INTEGRATION OF AN EXPLICIT FUNCTION ...
Page xxi
... progression 180. If the terms of a series decrease in magnitude and are alternately positive and negative , the series is con- vergent 235 236 237 240 181. u is convergent or divergent according as the ratio OF CONTENTS . xxi.
... progression 180. If the terms of a series decrease in magnitude and are alternately positive and negative , the series is con- vergent 235 236 237 240 181. u is convergent or divergent according as the ratio OF CONTENTS . xxi.
Page 17
... . ) Let n be negative ; that is , for n substitute -n ; [ x- " dx = f da PRICE , VOL . II . Xin x- ( n - 1 ) 1 = — = n - l ( n - 1 ) x2- D ( 2. ) Let n be fractional , n = 11. ] 17 INTEGRATION OF ALGEBRAICAL FUNCTIONS .
... . ) Let n be negative ; that is , for n substitute -n ; [ x- " dx = f da PRICE , VOL . II . Xin x- ( n - 1 ) 1 = — = n - l ( n - 1 ) x2- D ( 2. ) Let n be fractional , n = 11. ] 17 INTEGRATION OF ALGEBRAICAL FUNCTIONS .
Page 18
... 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 : we must therefore return to the principles of definite integration ...
... 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 : we must therefore return to the principles of definite integration ...
Page 48
... negative ; then dx 1 = ( a + bx— cx2 ) 3 4ac + b2 4 c2 - ( x – b 2 = sin - 1 { 2cx - b ( 4 ac + b2 ) S ' 2 c by reason of equation ( 61 ) . a ) } , ( 76 ) ( 77 ) dx Ex . 1 . = ( x2 + 2x 48 [ 37 . INTEGRATION OF -Integration of ...
... negative ; then dx 1 = ( a + bx— cx2 ) 3 4ac + b2 4 c2 - ( x – b 2 = sin - 1 { 2cx - b ( 4 ac + b2 ) S ' 2 c by reason of equation ( 61 ) . a ) } , ( 76 ) ( 77 ) dx Ex . 1 . = ( x2 + 2x 48 [ 37 . INTEGRATION OF -Integration of ...
Contents
1 | |
4 | |
18 | |
41 | |
48 | |
53 | |
71 | |
83 | |
322 | |
323 | |
324 | |
326 | |
327 | |
328 | |
330 | |
332 | |
85 | |
98 | |
104 | |
105 | |
108 | |
111 | |
117 | |
121 | |
123 | |
130 | |
134 | |
144 | |
150 | |
154 | |
155 | |
161 | |
169 | |
177 | |
184 | |
190 | |
197 | |
206 | |
210 | |
217 | |
222 | |
224 | |
231 | |
240 | |
249 | |
255 | |
256 | |
267 | |
279 | |
283 | |
287 | |
290 | |
302 | |
307 | |
308 | |
310 | |
311 | |
312 | |
313 | |
315 | |
316 | |
317 | |
319 | |
321 | |
333 | |
335 | |
337 | |
338 | |
339 | |
354 | |
366 | |
372 | |
376 | |
382 | |
388 | |
389 | |
395 | |
396 | |
403 | |
405 | |
411 | |
414 | |
420 | |
426 | |
427 | |
430 | |
436 | |
461 | |
482 | |
491 | |
511 | |
513 | |
520 | |
528 | |
556 | |
569 | |
589 | |
597 | |
606 | |
614 | |
615 | |
622 | |
629 | |
643 | |
651 | |
663 | |
666 | |
673 | |
680 | |
687 | |
693 | |
Other editions - View all
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