@ y } w r r s r { > r s r s v x | { C | { F { G r | x C...
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ȰɁɏɈȵɆȰ ɀȰȺȸɀȰɈȻȾȰ ȉİȤȞȚțȒȅȜȠțȜȒȡȦıȘȢ ɀɹɽʉɷʉʎɲʆʏɿʃɲʏɳʍʏɲʍɻʎ Ⱦɲʏɳʋɲʌɳɶʉʆʏɸʎʉʄʉʃʄɼʌʘʍɻ ɃʄʉʃʄɼʌʘʍɻɆɻʏʙʆɇʐʆɲʌʏɼʍɸʘʆ ɃʄʉʃʄɼʌʘʍɻʅɻͲɆɻʏʙʆɇʐʆɲʌʏɼʍɸʘʆ ɀɹɽʉɷʉʎɲʆʏɿʃɲʏɳʍʏɲʍɻʎ ɈɸʖʆɿʃɼɃʄʉʃʄɼʌʘʍɻʎͲɀʘʐʍɿɳɷɻʎɅʉʄ.Ⱦɲɽ.Ɉʅ.ɀɲɽɻʅɲʏɿʃ 2 .51 2 1 g(t) t Ʌɲʌɳɷɸɿɶʅɲ dx I x x ³ ɶɿɲx=0.5,t=2 ɶɿɲx=1,t=1 t dt t dt I x t t t ³ ³ ȶʍʏʘf(x)ʍʐʆɸʖɼʎʍʏʉ[ɲ,ɴ],g(t)ɷɿɲʔʉʌʀʍɿʅɻ ʙʍʏɸ: ɲ)g(ɶ)=ɲ,g(ɷ)=ɴ ɴ)ˁ˦˞˧˙˥ˢ x:ɲ d x d ɴ,ɿʍʖʑɸɿɶ d t d ɷɼɶ t ɷ ɶ)gʴ(t)ʍʐʆɸʖɼʎʍʏʉ[ɶ,ɷ]ɼ[ɷ,ɶ] f x dx fg t g t dt h t dt E G G D J J c ³ ³ ³ ʊʋʉʐh(t)=f(g(t))g'(t). ȺȵɏɆȸɀȰ Ⱥɹʏʉʐʅɸg(t)=1/t ȵʀʆɲɿgʚ(t) ʍʐʆɸʖɼʎ ʍʏʉ [1,2]
Transcript of @ y } w r r s r { > r s r s v x | { C | { F { G r | x C...
. . . 2
.5 1
2
1g(t)
t
dxIx x
x=0.5, t=2x=1, t=1
t dt t dtI xt t t
f(x) [ , ], g(t) :) g( )= , g( )=) x: x , t t) g (t) [ , ] [ , ]
f x dx f g t g t dt h t dth(t) = f(g(t)) g'(t).
g(t)=1/t
g (t)
[1,2]
. . . 3
f x dx
4. t=g 1(x) :
f x dx F g x c
3. :(i).To
. F(t) . :
f g t g t dt F t c4.
1. x=g(t) &
f g t g t dt2. :
(ii). .t x 1.
(iii). .1 .
. . . 4
. :
xI dxx x
tI dt t t t t t dtt t
t t t t t t t c
x x x x x x x c
x=t6 dx=6t5dt
. . . 5
t=z dzz
I t t dt t dt (2)
tta t t tt d t t (3)
x x x a c
x= t,dx= tdt
t x
t x
t x
. : I x dx (1)
. . . 6
( )
( )
f x dx f x dx
f x dx f x dx
f x dx f x dx
x= t .dx = dt, f(x) =f( t)
x=0 t= ,x= t=0 f x dx f a t dt
f x dx
:f x dx f a x dx ( )
. . . 7
:x dx
x xx xf x f x
x x x xx xI I dx dx
x x x xx x dx dxx x
nn n nf x x f x x x f x
f x dx f x dx = =0
: : nxdx n
. . . 8
: f x g x dx f x g x f x g x dx
••
• ( . . nx)•
.
g x df x f x g x f x dg x
u dv u v vdu
. . . 9
: x x dx
x x dx x d x
x x xd x
x x x x x c
x x x d x
uv
x x x x x dx
uv
x 1=t3 x x c
. . . 10
: nnI xdx
n n n nx x xd x x x n x xdx
n nx x n x x dx
n n nnI x x n x dx x dx
uv
n n nnI x dx x xdx xd x
nn n
nI I x x nn n
InIn 2
. . . 11
nn
n n
J x d x
x x xd x
: nnJ xdx
n nnJ J nn0
:J xdx:
J J J J
. . . 12
x x dx dx dxxx x x x x
•. .
P(x), Q(x)P x dxQ x
x dxx
xx c
. . . 13
x xI dxx x xA B dx
x x x
• ( ). .
A x x B x x x xx x x
x xx x x
=1,= 2,=2
. . . 14
PAQ
x= Q(x) : P xP x AQ x x Q x
Q(x)=(x )Q1(x), Q1( ) 0,:
Q x Q x x Q,
. . . 15
, 1, 2 5
Q x x x x x x xP x x x
PQ
PQ
PQ
I dxx x xx x x c
x xI c
x
. . . 16
x xI dxx x
• ( ). .
A B dxx xx x
A x x x x x x
I dx dx dxx xx
x d x x
. . . 17
x x x xI dx dxx x x x
• ( ). .
A x x x x x
xI dx dxx x
x dx x xdx dx dxx x x x
A B x dxxx x
12 .
. . . 18
xdt dt dt t t c e x ct t t
( , , .)
: ex=t, x=lnt
: x x
x xe eI dxe e
t dtt t
:
x xx xI dx dx x c e e cx x
• ex R(ex)
. . . 19
dt dt t c x cxtt t
: xI dxx
t dtt t
:x t x t
txttxt
dx dtt
• x, x R( x, x)
. . . 20
• 2x, 2x R( 2x, 2x)
:
x tx t
txt
xt
dx dtt
:
tI dtt t t
t t dt
t xI t c x c
xI dxx
. . . 21
tt dt t dt dt dt dt x ct t
:xI dx
x xt t dtt
x t
:ntx nndx t dtn x t
. . . 22
:
:n
ntx
tn
ndx nt dtt
nx tx
:
txt
xt
x tx
t tI dtt
tt=0 x=1 x=3.
:
t dtdxt
. . . 23
x xx x x t
ii) 1 2 , :
k t
x x t k
t k
iii) t, k :
t k z t k zkt
zt k z
t k z t k z
i) >0, : x x x t
. . . 24
:
I z dz z d z z d z
z z x x x x c
z zI dz d z czz z z
x x x x c
x t
t zzI dz z z dz z z c
z
t z dt z dz t co z.
tI d tt
.
. t z dzdtz
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