Page 298 - 1300 Math Formulas

CHAPTER 9. INTEGRAL CALCULUS

r
ê ∂ ñ ∂ ( = r á ⋅ ó ∂ ( + r à ⋅ ò ∂ ( + r
∂ ì ∂ ì ) î I ì ∂ ì ) î I ì ∂ ì ) î I ì â ⋅ I==
r
ê ∂ ñ ∂ ( = r á ⋅ ó ∂ ( + r à ⋅ ò ∂ ( + r
î ∂ î ∂ ) î I ì î ∂ ) î I ì î ∂ ) î I ì â ⋅ K==
=
1143. fÑ==íÜÉ==ëìêÑ~ÅÉ==p==áë==ÖáîÉå=Äó=íÜÉ=Éèì~íáçå=ò = ò ( óIñ )I=ïÜÉêÉ=

( ò ) ó I ñ ==áë==~==ÇáÑÑÉêÉåíá~ÄäÉ==ÑìåÅíáçå==áå==íÜÉ=Ççã~áå= ( a ) ó I ñ I=
íÜÉå==
• fÑ=p=áë=çêáÉåíÉÇ=ìéï~êÇI=áKÉK=íÜÉ=â-íÜ=ÅçãéçåÉåí=çÑ=íÜÉ=
åçêã~ä=îÉÅíçê=áë=éçëáíáîÉI=íÜÉå===
r
r
r
r
===== ∫∫ c ( ò I ) ó I ñ ⋅ p = ∫∫ c ( óIñ ò I )⋅ Çpå =
Ç
p p
r  ∂ò r ∂ò r r 
====== ∫∫ c ( = ò I ) ó I ñ ⋅ − á − à + â ÇñÇó I==


( a ) ó I ñ  ∂ñ ∂ó 
=
• fÑ=p=áë=çêáÉåíÉÇ=Ççïåï~êÇI=áKÉK=íÜÉ=â-íÜ=ÅçãéçåÉåí=çÑ=íÜÉ=
åçêã~ä=îÉÅíçê=áë=åÉÖ~íáîÉI=íÜÉå===
r
r
r
r
Ç
===== ∫∫ c ( ò I ) ó I ñ ⋅ p = ∫∫ c ( óIñ ò I )⋅ Çpå
p p
r  ∂ò r ∂ò r r 
====== ∫∫ c ( = ò I ) ó I ñ  ⋅  á + à − â ÇñÇóK==

( a ) ó I ñ  ∂ñ ∂ó 
=
1144. ( ∫∫ c å ) ⋅ Çp = ∫∫ mÇóÇò + nÇòÇñ + oÇñÇó =
r
r
p p
= ∫∫ ( m α + n Åçë β + Åçë γ Çp I==
) Åçë
o
p
ïÜÉêÉ= ( m ò I I= ( ó ) ò I I= ( ó ) ò I =~êÉ=íÜÉ=ÅçãéçåÉåíë=çÑ=
I
I
o
) ó I ñ
ñ
n
ñ
r
íÜÉ=îÉÅíçê= ÑáÉäÇ= c K==
γ
β
Åçë α I= Åçë I= Åçë ==~êÉ=íÜÉ= ~åÖäÉë= ÄÉíïÉÉå=íÜÉ=çìíÉê=ìåáí=
r
åçêã~ä=îÉÅíçê= å =~åÇ=íÜÉ=ñ-~ñáëI=ó-~ñáëI=~åÇ=ò-~ñáëI=êÉëéÉÅí-
áîÉäóK=
=
288