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of INFINITE types siexdx -3 ¥eEmmmmpeople.math.umass.edu/~johnston/M128F18/128F18-10-1.pdf ·...
Transcript of of INFINITE types siexdx -3 ¥eEmmmmpeople.math.umass.edu/~johnston/M128F18/128F18-10-1.pdf ·...
Improper Integrals
-3types A INFINITE interval of integration
siexdx ¥eEmmmm⇐ Ex
2) fix become INFINITE onthe interval
soax
'
¥€÷e,3) Both situations hold
s! # dx t¥
Et .
fod×=SoEdk%
. .fexdx - - Etc
*
=- Elo Efendi! '¥9
,¥7 '
= .
-
Lexi .
".
"
g
= - [ e-"
-"
-e-
o]=
- [ o - T!e→"=iinex=oT=
x - soA FINITE # and
fine'=fi;s¥=o we say the integralConRG
Ee. S! 'T dx O'
tix :t¥±a:Exit: "
× .
= In I - In"
o
' '= O - In
"
o
"
=o - C - a ) =
In"
o
' '
=L In X = - 0 Not afinite # so
we say that the
integral
Ii;nohx=- d
DIUERGfind In x
-- a -
exi.si#dx--i8x-adxsxIIitItI
'
t÷= I
"
= - I'
Ii.
"
÷=¥÷=±= - [ x' Ii
."
] x' - I
= - [ ¥.
-¥3'x'
tx=o= - [ o - D= ⑤
in Finite # sothe Mtesrd/Con1uER6EJ
.
Integration By Parts .
-
-
. Sudu=uv-Sudu#where
does the formula come from ?
Pffudygti ¥ [ fang 3 = fang 'm t gunfix )
⇒ fixigcx, = f¥x[fungus]dx=ffixdxt fgcxiffxidx
solve for this term
{ fang 's dx =fix gcxl - f gcxiftxidx
TE IT THE
u -
- fan "
gudu=uV-Sv#fda -
-f 'M DX
=
"
known"
-
"
Easier"
Island .¥to