CHAPTER 9. INTEGRAL CALCULUS
- mêçéÉêíáÉë=çÑ=iáåÉ=fåíÉÖê~äë=çÑ=sÉÅíçê=cáÉäÇë=
∫()()⋅ =−∫ ⋅
−` `
c Çê c Çê
r r r r
I==
ïÜÉêÉ=-`=ÇÉåçíÉ==íÜÉ=ÅìêîÉ=ïáíÜ=íÜÉ=çééçëáíÉ=çêáÉåí~íáçåK=
=
∫( ⋅ )= ∫( ⋅ )=∫( ⋅ )+∫( ⋅ )
` `N∪`O `N `O
c Çê c Çê c Çê c Çê
r r r r r r r r
I==
ïÜÉêÉ=`=áë=íÜÉ=ìåáçå=çÑ=íÜÉ=ÅìêîÉë=`=~åÇ=N `K==O
=
- fÑ=íÜÉ=ÅìêîÉ=`=áë=é~ê~ãÉíÉêáòÉÇ=Äó=ê(í)= ñ(í)Ió(í)Iò(í)
r
I=
α≤íI=íÜÉå==≤β
∫ + + =
`
mÇñ nÇó oÇò =
∫ ()() () () ()() () () ()() () ()
β
α
= + + Çí
Çí
Çò
oñíIóíIòí
Çí
Çó
nñíIóíIòí
Çí
Çñ
mñíIóíIòí
=
- fÑ=`=äáÉë=áå=íÜÉ=ñó-éä~åÉ=~åÇ=ÖáîÉå=Äó=íÜÉ=Éèì~íáçå=ó=Ñ()ñ I=
íÜÉå==
∫ ∫ () ()() ()
+ = +
Ä
` ~
Çñ
Çñ
ÇÑ
mÇñ nÇó mñIÑñ nñIÑñ K==
=
- dêÉÉå∞ë=qÜÉçêÉã=
∫∫ =∫ +
∂
∂
−
∂
∂
o `
ÇñÇó mÇñ nÇó
ó
m
ñ
n
I==
ïÜÉêÉ=c m()ñIóá n(ñIó)à
r r r
= + = áë= ~= Åçåíáåìçìë= îÉÅíçê= ÑìåÅ-
íáçå=ïáíÜ==Åçåíáåìçìë==Ñáêëí=é~êíá~ä==ÇÉêáî~íáîÉë=
ó
m
∂
∂
I=
ñ
n
∂
∂
=áå=~=
ëçãÉ=Ççã~áå=oI=ïÜáÅÜ=áë=ÄçìåÇÉÇ=Äó=~=ÅäçëÉÇI=éáÉÅÉïáëÉ=
ëãççíÜ=ÅìêîÉ=`K==
=
=
