297 

 P r o b l e m a 3. 



\. 1. Si fucrit V=r/a7/ (xx -4- 7/j/)M2^r^j^--] investi- 

 gare intégrale f Y dx ["dx^i^- 



S 1 u t i 0. 



Cum sit V ceita functio binarum variabilium x et y, quae- 

 ramus ejus diiferentiale , si tara x quara y variabiles statuantur, 

 eritque 



dV =z: dy (xx -\-ytjY -+- inxdxfdy {xx ~\-yyY~'^ 

 cujus pars posierior signo summatoiio aflecta ad formam , quam 

 V vocavimus reducitur, ponendo 



fdy i^^ + yyT~ * =: ^yixx -\- ijyY -\- Bfdy ixx -\- yiff- 



ac differenliatione instituta rcperietur fore Azu — ^^^ei'Q':^:.-^^- 

 quibus valoribus substitutis positoque ■/ 1 — xx loco y habebimus 



j ^j ^ 1 jay 2nxx ' 2nxx 



Hoc va'.ore substituto habebimus hanc aequationem resolvendam : 



aVr= — ^^^-f- (2n+ 1)Y^ 

 xV 1 ■ — ■ XX X 



qua ducta in multiplicatorem x ^^ * fiet integrabilis , piodibitque 



^ -^ V i — xx 



ut supra §■ 5. invcnimus, unde pro terminis integrationis stabilitis 

 sequitur Ibre 



,-^r■^ rab xrrrOT , w 



§.8. Manente V = /r)2/ (:r x -+- t/î/)" [H;' ^ ^ ° -j-^-] mm«- 



rab x: 



P r O b l e m a Â. 



gra/e intégrale f\xdx [^j^""]. 



S 1 u t i 0. 

 Cum supra §. 5. invenerimus 



.fK/^p/. a«x JVÏÉmoiret de VAcad. "^" 



