for fgcxlftxsdx gaddpeople.math.umass.edu/~johnston/M128F19/7.4a.pdf71: Integration by Parts Product...
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71 : Integration by Parts - Product Rule : ¥ ( fix , .gcxD= fixing 'cx , t g HI . fix , ÷ for { fan . g 'm dx = f # ( fan gadd , - fgcxlftxsdx stacking = EYE 'T ' - SE " !4¥×v=* I d¥ - - Stx , S a du = U V - S Uda do - - g ' cxidx t.int#ieTie7 Iii . du - - ffxidx
Transcript of for fgcxlftxsdx gaddpeople.math.umass.edu/~johnston/M128F19/7.4a.pdf71: Integration by Parts Product...
71 : Integration by Parts-
Product Rule : ¥ ( fix , .gcxD= fixing 'cx, t g HI . fix ,
÷ for
{ fan . g 'm dx = f # (fangadd ,-fgcxlftxsdx
stacking= EYE'T' -
SE"
!4¥×v=*I
d¥ -- Stx ,
S a du =U V - S Uda do -
- g'
cxidx
t.int#ieTie7 Iii .
du -
- ffxidx
Exe'. S XI dx Se
'
"dx=fze'"
toway ⇒v= Een
✓da1dxduEe"dxJ
Sxe "d× =UU - Suda
- = x. Ee"
- SEE ? Idx
original=z×eH - Ise "dx
.. -
-- hnrewitegral
= Exert - I . tea 't C
=Hxe"-¥e"tcT_
Examplesv= ?
a) 51¥ dx" ¥4du
-7# dx
a = In X
lol S lnxdx u=lnx
c) Staetdt u=f
a) S hftadx = Slnx . # dx
= S In x - I 'd x
I Tv 5×-4=5"
U --
In X v == - Yx It ,
TC
du Etxdx du-7x' dx
= a v - Suda= xnxx.tl - S HI dx
= - tuff t S xtdx = -1¥ - f t C
⇒ ¥ ( If - It c) =' ¥ C CHECK ! )
b) Slnxtdx = au - Sudain -
u du =dnx ) . X - Sxstxdxwin
u= lux V=XU du
t r
du -_ txdx du -- adx = xlnx - Side
= xlnx - Xtc
checky:
¥fxlnx -
xtd-x.lhxl.tl/nxl.kx5-Ito--X.txtClnxl.I-I--1tlnx-I=/lnxJ
