1300 Math Formulas

(Dana P.) #1
CHAPTER 9. INTEGRAL CALCULUS


  1. fÑ=íÜÉ=ëìêÑ~ÅÉ=p=áë=ÖáîÉå=áå=é~ê~ãÉíêáÅ=Ñçêã=Äó=íÜÉ=îÉÅíçê=
    ê()ñ()()ìIîIóìIîIò(ìIî)
    r
    I==íÜÉå==íÜÉ==ä~ííÉê=Ñçêãìä~=Å~å=ÄÉ=
    ïêáííÉå=~ë==


()


()

ÇìÇîI

î

ò
î

ó
î

ñ

ì

ò
ì

ó
ì

ñ

m n o
c åÇp mÇóÇò nÇòÇñ oÇñÇó
p p aìIî

∫∫ ∫∫ ∫∫














⋅ = + + =


r r

ïÜÉêÉ=()ìIî =ê~åÖÉë=çîÉê=ëçãÉ=Ççã~áå=a(ìIî)=çÑ=íÜÉ=ìî-
éä~åÉK=
=


  1. aáîÉêÖÉåÅÉ=qÜÉçêÉã=


∫∫ ⋅ =∫∫∫()∇⋅


p d

c Çp cÇs

r r r
I==

ïÜÉêÉ==
c()()ñIóIò =mñIóIòIn(ñIóIò)Io(ñIóIò)

r
===
áë==~==îÉÅíçê==ÑáÉäÇ==ïÜçëÉ==ÅçãéçåÉåíë==mI==nI==~åÇ==o==Ü~îÉ==
Åçåíáåìçìë=é~êíá~ä=ÇÉêáî~íáîÉëI==

ò

o
ó

n
ñ

m
c


+




+




∇⋅ =


r
==

áë==íÜÉ==ÇáîÉêÖÉåÅÉ==çÑ==c

r
I==~äëç==ÇÉåçíÉÇ==Çáîc

r
K==qÜÉ==ëóãÄçä=

∫∫ =áåÇáÅ~íÉë==íÜ~í=íÜÉ=ëìêÑ~ÅÉ=áåíÉÖê~ä=áë=í~âÉå=çîÉê=~=ÅäçëÉÇ=


ëìêÑ~ÅÉK==
=


  1. aáîÉêÖÉåÅÉ=qÜÉçêÉã=áå=`ççêÇáå~íÉ=cçêã=


∫∫ ∫∫∫ 











+




+




+ + =


p d

ÇñÇóÇò
ò

o
ó

n
ñ

m
mÇóÇò nÇñÇò oÇñÇó K==

=


  1. píçâÉ∞ë=qÜÉçêÉã=


∫ ⋅ =∫∫()∇× ⋅


` p

c Çê c Çp

r r r r
I==
Free download pdf