Page 299 - 1300 Math Formulas

CHAPTER 9. INTEGRAL CALCULUS

1145. fÑ=íÜÉ=ëìêÑ~ÅÉ=p=áë=ÖáîÉå=áå=é~ê~ãÉíêáÅ=Ñçêã=Äó=íÜÉ=îÉÅíçê=
r
ê ( ( ) î I ì ( ó I ) î I ì ò I ( îIì ) I==íÜÉå==íÜÉ==ä~ííÉê=Ñçêãìä~=Å~å=ÄÉ=
)ñ
ïêáííÉå=~ë==

m n o
r
∫∫ ( c r ) å ⋅ Çp = ∫∫ mÇóÇò + nÇòÇñ + oÇñÇó = ∫∫ ∂ ñ ∂ ∂ ó ∂ ∂ ò ∂ ÇìÇî I
p p ( a ) î I ì ì ì ì
ñ ∂ ó ∂ ò ∂
î ∂ î ∂ î ∂
ïÜÉêÉ= ( ) î I ì =ê~åÖÉë= çîÉê=ëçãÉ= Ççã~áå= ( îIìa )=çÑ= íÜÉ= ìî-

éä~åÉK=
=
1146. aáîÉêÖÉåÅÉ=qÜÉçêÉã=
r
r
r
∫∫ c ⋅ p ∫∫∫ ( = ∇ c ) ⋅ ÇsI==
Ç
p d
ïÜÉêÉ==
r
c ( ) ó I ñ = m ( ò I ò I ) ó I ñ I n ( óIñ ò I ) ( óIñoI ) ò I ===
áë==~==îÉÅíçê==ÑáÉäÇ==ïÜçëÉ==ÅçãéçåÉåíë==mI==nI==~åÇ==o==Ü~îÉ==
Åçåíáåìçìë=é~êíá~ä=ÇÉêáî~íáîÉëI==
r ∂ m ∂ n ∂ o
∇ ⋅ c = + + ==
ñ ∂ ó ∂ ò ∂
r r
c
áë==íÜÉ==ÇáîÉêÖÉåÅÉ==çÑ==c I==~äëç==ÇÉåçíÉÇ==Çáî K==qÜÉ==ëóãÄçä=
∫∫ =áåÇáÅ~íÉë==íÜ~í=íÜÉ=ëìêÑ~ÅÉ=áåíÉÖê~ä=áë=í~âÉå=çîÉê=~=ÅäçëÉÇ=

ëìêÑ~ÅÉK==
=
1147. aáîÉêÖÉåÅÉ=qÜÉçêÉã=áå=`ççêÇáå~íÉ=cçêã=
 ∂m
∫∫ mÇóÇò + nÇñÇò + oÇñÇó = ∫∫∫ + ∂n + ∂o  ÇñÇóÇò K==


p d  ∂ñ ∂ó ∂ò 
=
1148. píçâÉ∞ë=qÜÉçêÉã= r
r
r
r
∫ c ⋅ ê ∫∫ ( = ∇ ) ×c ⋅ p I==
Ç
Ç
` p

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