Page 289 - 1300 Math Formulas

CHAPTER 9. INTEGRAL CALCULUS

1127. ^êÉ~=çÑ=~=oÉÖáçå=o=_çìåÇÉÇ=Äó=íÜÉ=`ìêîÉ=`=

p = ∫∫ ÇñÇó = N ∫ ñÇó − óÇñ =
o O `
=
1128. m~íÜ=fåÇÉéÉåÇÉåÅÉ=çÑ=iáåÉ=fåíÉÖê~äë= r r r r
qÜÉ= äáåÉ=áåíÉÖê~ä= çÑ=~=îÉÅíçê= ÑìåÅíáçå= c = á m + n à + o â =áë=
ë~áÇ=íç=ÄÉ=é~íÜ=áåÇÉéÉåÇÉåíI=áÑ=~åÇ=çåäó=áÑ=mI=nI=~åÇ=o=~êÉ=
Åçåíáåìçìë=áå=~=Ççã~áå=aI=~åÇ=áÑ=íÜÉêÉ=Éñáëíë=ëçãÉ=ëÅ~ä~ê=
ÑìåÅíáçå==ì = ì ( óIñ ) ò I ==E~==ëÅ~ä~ê==éçíÉåíá~äF==áå==a==ëìÅÜ=íÜ~í=

r ∂ ì ∂ ì ∂ ì
c = Öê~Ç ì I=çê= = m I= = n I= = o K==
ñ ∂ ó ∂ ò ∂
qÜÉå==
r
r
∫ c () Çê ⋅ r ∫ mÇñ + nÇó + oÇò = ì ( ) ì_ − ( )K==
ê =
^
` `
=
1129. qÉëí=Ñçê=~=`çåëÉêî~íáîÉ=cáÉäÇ=
r
^=îÉÅíçê=ÑáÉäÇ=çÑ=íÜÉ=Ñçêã=c = Öê~Ç ì =áë=Å~ääÉÇ=~=ÅçåëÉêî~íáîÉ=
r r r r
ÑáÉäÇK=qÜÉ=äáåÉ=áåíÉÖê~ä=çÑ=~=îÉÅíçê=ÑìåÅíáçå=c = á m + n à + o â =
áë=é~íÜ=áåÇÉéÉåÇÉåí=áÑ=~åÇ=çåäó=áÑ==
r r r
á à â
r ∂ ∂ ∂ r
Åìêä c = = M K==
ñ ∂ ó ∂ ò ∂
m n o
=
fÑ=íÜÉ=äáåÉ=áåíÉÖê~ä=áë=í~âÉå=áå=ñó-éä~åÉ=ëç=íÜ~í==
∫ mÇñ + nÇó = ì ( ) ì_ − ( )I==
^
`
íÜÉå=íÜÉ=íÉëí=Ñçê=ÇÉíÉêãáåáåÖ=áÑ=~=îÉÅíçê=ÑáÉäÇ=áë=ÅçåëÉêî~íáîÉ=
Å~å=ÄÉ=ïêáííÉå=áå=íÜÉ=Ñçêã==
∂ m = ∂ n

ó ∂ ñ ∂ K==
=

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