Thiết kế bài giảng giải tích lớp 12 tập 2

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GIAI TICH
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NHA
XUAT
BAN
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TRAN VINH
THIET KE BAI GIANG
GIAI TICH
TAP HAI
NHA XUAT BAN HA NOI

Chi/dNq
III
NGUYEN HAM - TICH PHAN VA
UNC
DUNG
Phan 1
NHJtXG VAX
DE CUA
CHMfONG
I.
NOI
DUNG
Noi dung chinh cua
chucung
3 :
Nguyen ham : Dinh nghia ;
tinh
chat;
cac nguyen ham
ccf
ban ; cac phucmg phap
tinh nguyen ham.
Tich phan : Dinh nghia ; cac tinh chat cua tich phan ; cac phuang phap tinh
tich phan.
"
Lftig
dung cua tich
phSn
: Bai toan dien tich, bai toan thi tich.

n.
MUC TIEU
1.
Kien
thiirc
Nam dugc
toan bo kien thiic co ban trong chuong da neu tren, cu the :
Nam
viing dinh nghia nguyen ham, cac nguyen ham co ban, cac tinh chat ciia
nguyen ham.
• Dinh nghia tich phan, cac tinh chat
ciia
tich phan,
ung
dung ciia tich phan, moi
quan he giiia tich phan va nguyen ham.
M6t
s6' ling dung tich phan trong hinh hoc : Tinh dugc dien tich
hinh
phang,
the tich vat the trong khong gian.
2.
KT nang
van
dung cac nguyen ham co ban de
tinh
cac nguyen ham.
Van dung thanh thao cong thiic Niuton - Laibonit de tinh tich phan. Moi
quan he giiia dao ham va nguyen ham.
Van dung tich phan de tinh dien tich hinh phang va the tich ciia vat the.

3.
Thai do
Tu giac. tich
cue,
dgc lap va
chii
dgng phat hien ciing nhu
ITnh
hoi kien" thiic
trong qua trinh hoat dgng.
Cam nhan dugc su
cSn
thiet cua dao ham trong viec khao sat ham so.
Cam nhan dugc thuc te cua toan hgc, nhat la doi vdi dao ham.
PHan
2.
CAC BAI
SOA]!!^
§1.
Nguyen
ham
(tiet 1, 2, 3, 4, 5)
I. MUC TIEU
1.
Kien thurc
HS nam duac :
Nh6
lai
each
tinh dao ham cua ham sd.

• Dinh nghia nguyen ham.
• Cac tinh chat ciia nguyen ham.
Mot so' nguyen ham co ban.
Cac phuong phap tinh nguyen ham : Phuong phap doi bien sd va phuong
phap nguyen ham tiing phan.
2.
KT nang
HS tinh thanh thao cac nguyen ham co ban.
Tinh dugc nguyen ham dua vao phuong phap doi bien sd va phuong phap
nguyen ham tiing phan.
3.
Thai do
Tu giac, tich
cue
trong hgc tap.
Biet phan biet ro cac khai niem co ban va van dung trong tiing trudng hgp cu the.
"
Tu duy cac va'n de cua toan hgc mot
each Idgic
va he thdng.
n.
CHUAN BI CUA GV VA HS
1.
Chuan bj
ciia
GV
Chuan bi cac
cau
hoi ggi mo.
Chuan bi pha'n mau, va mdt sd dd diing khac.

2.
Chuan bj cua HS
Can dn lai mot sd kien thiic da hgc ve dao ham.
ra. PHAN PHOI
THCJI
LUONG
Bai nay chia lam 5
tiet:
Tiet 1 : Tic dau den hit
miic
2 phdn I.
Tiet 2 : Tiep theo den het phdn I.
Tiet 3 : Tiep theo den het muc I phdn II.
Tiet 4 : Tiep theo den het phdn II.
Tiet 5 : Bdi tap
IV TIEN TRINH DAY HOC
A. DAT VAN
OE
Cau hoi 1
Xet tinh diing - sai cua cac cau sau day :
a) Ham sd y =
In(cosx)
cd dao ham y' = -tanx.
b) Ham sd y =
In(cosx)
cd dao ham y' = -cotx.
Cau hoi 2
Chohamsdy=
3''""
a) Hay tinh dao ham cua ham sd da cho.

b) Chiing minh rang ham sd y
=
x3''"''
cd dao ham la y' =
3''""
GV:
Ham y
=
xS^'""
ggi la nguyen ham ciia ham sd y' =
3^'""
B.
BAi
Mdl
I NGUYEN
HAM
VA TINH CHAT
HOATDONC1
1.
Nguyen ham
•
Thuc hien
f\
1
trong
5'
Hoat dgng cua GV
Cau hoi 1
Tim mot ham sd F(x)
F(x)

= 3x2
Cau hoi 2
Tim mot ham sd F(x)
FYY^
—
r
vx;
—
cos X
ma
ma
Hoat dong cua HS
Ggi y tra loi cau hoi 1
GV ggi mot vai HS tra
Idi.
Bai toan
nay cd nhieu dap sd.
Tong quat : F(x) =
x^
+ C trong do
C la hang sd bat
ki.
Ggi
y tra Idi cau hoi 2
Lam tuong tu
cau
a.
In
X
F(x)

= -^
cos X
• GV neu dinh nghia :
Cho hdm
sof(x)
xdc dinh tren K
Ham
soF(x)
duac ggi
Id nguyen
hdm cda hdm
sof(x)
tren K neu
F '(x) - f(x) vai
mgi
x e K
• GV neu va thuc hien vf du
1,
GV cd the
lay
mdt vai vi du khac.
HI.
Tim
nguyen ham ciia ham sd y
=
x.
H2.
Tim
nguyen ham cua ham sd y
=

x
H3.
Tim
nguyen ham cua ham sd y = x
H4.
Tim
nguyen ham ciia ham sd y =
x"
4
•
Thuc Men
f\2
trong
5'.
Hoat dong ciia GV
Cau hoi 1
Tim mot ham sd F(x) ma
F(x) =
2x.
Cau hoi 2
Tim
mot ham sd F(x) ma
V{x)=
X
Hoat dong
ciia
HS
Ggi y tra loi cau hoi 1
GV ggi mot vai HS tra
Idi.

Bai toan
nay cd nhieu dap sd.
Tong quat : F(x)
= x^
+C trong dd
C la hang sd bat ki.
Ggi y tra loi cau hoi 2
Lam tuong tu
cau
a.
F(x)
= hix
+ C.
H5.
Tim
nguyen ham ciia ham sd y = sin x.
H6.
Tim
nguyen ham cua ham sd y = cosx.
1
H7.
Tim nguyen ham ciia ham sd y
2Vx
N/2
H8.
Tim nguyen ham ciia ham sd y = x
• GV neu dinh li
1:
Neu F(x)
Id

mot nguyen hdm cua hdm
sof(x)
tren K thi vai moi hang so
C, hdm
soG(x) =
F(x) + C
cUng Id
mot nguyen hdm cda f(x) tren K
H9.
Biet ham sd cd mdt nguyen ham la y = sin
x.
Hay tim nguyen ham cua ham sd dd.
HIO.
Biet ham sd cd mdt nguyen ham la y
=
cosx. Hay tim nguyen ham cua ham
sd
dd.
1
Hll.
Biet ham sd cd mdt nguyen ham la y
= ^^ '^
. Hay tim nguyen ham cua ham sd dd.
H12.
Biet ham sd cd mdt nguyen ham la y
= ^
. Hay tim nguyen ham ciia ham sd dd.
• Thuc hien
Sgr 3
trong

5'.
Hoat dgng ciia GV
Cau hdi 1
Hoat dgng
ciia
HS
Ggi y tra loi cay hoi 1
Tinh dao ham ciia ham sd :
y = G(x).
Cau hoi 2
Hay ket luan.
{G{x)y =
[Fix)
+
C]'
=
F'(x)
+
C' =
fix),xeK.
Ggi y tra loi cau hoi 2
GV tu ket luan.
GV neu dinh li 2:
Neil F(x)
Id
mot
nguyen
hdm cua hdm
sof(x)
tren K thi moi

nguyen
hdm
cua
f(x) tren K deu co
dgng
F(x)
+
C, vai C
Id
mot hang so.
De chiing minh dinh li, GV neu va'n
66
de HS chiing minh.
GV neu ki hieu :
^f(x)dx -
Fix)
+
C.
• GV neu
chii
y trong SGK.
• De thuc hien vi du 2, GV cd the neu cac vi du khac hoac cho HS tu neu vi du va
dat cac cau hdi sau :
H13.Tinh
J3xdx.
H14.Tinh
Jkdx.
H15.Tinh f-dx.
Hld.Tinh
f-^dx

•'2Vx
HOAT DONG
2
2.
Tinh
chat ciia nguyen ham
• GV neu tinh chat
1:
(
lf{x)dx)'
=
fix) ;
jf'ix)dx -
fix)
+
C.
HI7.
Hay chiing minh cac tinh chat tren.
H18.
Tinh
ftanxdx.
• GV neu va cho
HS
thuc hien vi du 3 hoac cd the lay nhiing vi du khac.
• GV neu tinh chat 2 :
\kfix)dx
= k
\fix)dx
De chiing minh tinh chat nay, GV
cSn

dua ra cac cau hdi sau :
HI9.
Tinh dao ham hai ve.
H20.
Chiing minh dao ham hai ve bang nhau.
• GV neu tinh chat 3 :
j[fix)
±
gix)]dx =
\fix)6x ±
jgix)dx.
•
Thuc
hien
"pt 4 trong
5'
Hoat dgng cua GV Hoat dgng ciia HS
Cau hoi 1
Tinh dao ham cua ham
so d mdi ve.
Cau hoi 2
Hay lam tuong tu ddi
vdi trudng hgp dau
trir.
Ggi y tra loi cau hoi 1
[\fix)Ax+
\gix)6x\
=
[\fix)6x)
+[\gix)dx] ^fix) +

gix).
Ggi
y
tra loi cau hoi 2
[lfix)dx
-
jgix)dx]
= fix) - gix).
• GV neu va thuc hien vi du 4. GV cd the thay bdi vi du khac.
H21.
Tinh
J (cos x +
sin x)dx .
H22.
Tinh
[(cos x +
tan x)dx .
H23.
Tinh
[(cosx
-
vx)dx
.
H24.Tinh
|(x^+x +
l)dx.
10
nOATiyDNG3
3.
Sii

ton tai nguyen ham
• GV
n6u
dinh li 3:
Moi hdm
sof(x)
lien tuc tren K deu co
nguyen
hdm tren K
• Thuc
hidn
vi du 5:
2
H25.
Chiing minh ham sd y =
x ^
cd nguyen ham. Tinh nguyen ham cua ham sd dd:
H26.
Chiing minh ham sd y =
—z—
cd nguyen
ham.
Tinh
nguyen ham ciia
ham sd
dd.
sin X
• GV cho HS tinh
nguyfen
ham va dien vao bang sau :

••"';:-v '^-
fix) '"\ :.:,jr
0
ax«-^
1
x
e^
a*lna
ia>
0,a^l)
cosx
—siruc
1
cos x
1
sin x
:
fix)
+
C
11
• Thuc hien vi du
6
trong 5'
Cau a.
Hoat dgng ciia GV
Cau hdi 1
Tinh nguyen ham ciia ham so:
y=
ly}

Cau hoi 2
Tinh nguyen ham ciia ham sd:
1
Cau hoi 3
Tinh nguyen ham ciia ham so
da cho.
Hoat dgng ciia HS
Ggi y tra loi cau hoi 1
[2x2dx =
-x^
J
3
Ggi y tra loi cau hdi 2
1
^ '
[-^L=dx-
[x
3dx-3x3
Ggi y tra loi cau hoi 3
HS
tu tinh.
cau
b. HS tu tinh tuong tu.
II.
PHUONG PHAP TINH NGUYEN HAM
HOAT
DONG 4
1.
Phuong phap doi bien sd
•

Thuc
hien
^.
6
trong
5'
Hoat dgng cua GV
Cau hdi 1
Dat u =
X
-
1,
tinh du
Cau hoi 2
Tinh
|(x-l)'°dx.
Hoat dgng ciia HS
Ggi y tra loi cau hoi 1
Ta cd du
=
u'dx
=
dx.
Ggi y tra loi cau hoi 2
12
[(x-iyOdx^[u'Odu = -ui'+C
= l(x-i)"+C
U
caub.
Hoat dgng

ciia
GV
Cau hdi 1
Dat x
=
e'
tinh
dt.
Cau hoi 2
Tinh [
dx.
•'
X
Hoat dgng cua HS
Ggi y tra loi cau hdi 1
Ta cd t
= Inx
=> dt
= —dx
X
Ggi y tra loi cau hdi 2
[^^dx=[tdt=^2^C=^ln2x
+ C
J
X
J
2 2
•
GV neu
dinh

li
1:
Neil
\fiu)du
= Fiu) + C
vdu
=
u(x)
la hdm so co dao hdm
lien
tuc
thi
\fiuix))u
'ix) dx =
Fiuix))
+ C.
H27.
Hay
chiing minh dinh
ii
tren.
•
GV neu he qua:
f
1
\fiax+
b)dx
=—Fiax+
b) + C
(a ^

0).
J
a
H28.
Hay
chiing minh
he qua
tren.
•
GV cho
HS thuc hien
vi du 7. GV cd the
thay
bdi vi du
tuong
tu.
•
Ddi vdi
chii
y
trong SGK,
GV neu va
nhSii
manh dieu
nay :
Mgi bien
sau khi
thay
ddi
trong

qua
trinh
tinh
toan, song
ket qua
cud'i ciing phai
la
bien
ban dau.
• Thuc hien
vi du 8
trong
5'
13
Hoat dgng ciia GV
Cau hdi 1
Nen dat bien nao bdi bien u.
Cau hdi 2
Tinh nguyen ham ciia ham sd
da cho.
Hoat dgng ciia HS
Ggi y tra
Idi
cau hdi 1
Datu
= x- 1.
Ggi y tra
Idi
cau hdi 2
HS tu tinh.

H29.Tinh
f(3x + l)dx
H30.Tinh
f(x +
l)dx
H31.Tinh jtanxdx.
HOATD0NG5
2.
Phifong
phap nguyen ham tiimg
phSn
•
Thuc
hien
-^ 7trong
5'
Hoat dgng ciia GV
Cau hdi 1
Tinh
\ix cos
xYdx.
Cau hdi 2
Tinh
fcosxdx.
Cau hdi 3
Tinh
[xsinxdx.
Hoat dgng cua HS
Ggi y tra loi cau hdi 1
Ta cd

Ux
cos x)'dx = x cos
x + Ci
Ggi y tra
Idi
cau hdi 2
[cosxdx
=
sinjc
+
C2,
Ggi y tra loi cau hdi 3
\x
sin xdx = -x
cos
x
+
sin x + C
• GV neu dinh li 2 :
Neu hai hdm
sou
= u(x)
vdv
= v(x) co dao hdm lien tuc tren K thi
\uix)v\x)dx
= uix)vix) -
^u\x)vix)dx.
14
H32.
Hay chiing minh dinh li tren.

• GV neu
chii
y :
[udi;
- uv -
\vdu.
• Thuc hien vi du 9 trong 7' Day la vi du quan trgng, GV nen hudng dan cu the
cau a.
Hoat dgng
ciia
GV
Cau hdi 1
Dat u va dv hgp
If.
Cau hdi 2
Van dung dinh
If,
hay
tfnh
nguyen ham ciia ham sd tren.
Hoat dgng ciia HS
Ggi y tra loi cau hdi 1
Dat u = X, dv =
e^'dx
Ggi y tra loi cau hdi 2
Jxe^'dx =
xe''
-
fe''dx
= xe"

-e"
+
C.
caub.
Hoat dgng ciia GV
Cau hdi 1
Dat u va dv hgp If.
Cau hdi 2
van
dung dinh
If
hay tfnh
nguyen ham ciia ham so tren.
Hoat dgng cua HS
Ggi y tra loi cau hdi 1
Dat u = X, dv = cosxdx
Ggi y tra loi cau hdi 2
[x cos X d X
=
X sin X + cos x +
C.
Cau c.
Hoat dgng cua GV
Cau hdi 1
Dat u va dv hgp If.
Cau hdi 2
Van dung dinh
If
hay tfnh
nguyen ham cua ham sd tren.

Hoat dgng ciia HS
Ggi y tra loi cau hdi 1
Dat u = Inx, dv = dx
Ggi y tra loi cau hdi 2
[in X d X
=
X In X
-
j
dx
= x In x -
-x
+
C.
15
• Thuc hien
GL
8
trong
5'
GV cho HS tu dien vao bang. Ket qua nhu sau:
u
dv
jPix)e''dx
P(x)
e^dx
[P(x)cosxdx
P{x)
cosxdx
JP(x) In

xdx
Inx
Prxjdx
HOAT
DONG 6
TOM
T^
B^l
H9C
1.
Cho ham
so
fix) xac dinh tren K
Ham sd
F(x)
dugc ggi la nguyen ham ciia ham sd fix) tren K neu F 'ix) - fix)
vdi mgi x e K
2.
Neu Fix) la mdt nguyen ham cua ham sd fix) tren K thi vdi mdi hang so C,
ham sd G(x) = Fix)
+
C ciing la mdt nguyen ham ciia fix) tren K
h) Neu Fix) la mdt nguyen ham cua ham so fix) tren K thi mgi nguyen ham cua
fix) tren K deu cd dang Fix) + C, vdi C la mdt hang sd.
3.
(
jfix)dx)'
-
fix) ;
lf'ix)dx -

fix)
+
C.
\kfix)dx
=
k\fix)dx\;
I \[fix)±gix)\dx
=
\fix)dx±
\gix)dx.
5.
Mgi ham sd fix) lien tuc tren K deu cd nguyen ham tren K
6.
J0dx
= C
\dx = X
+ C
1"
fi^
la^dx
= + C (a > 0, a
^
1)
J
In
a
Icosxdx =
sinx+ C
16
fr"Hr

r"+l
-I-r'
rr/3t H
J a + 1
—
dx =
Inlxl
+ C
Jx ' '
fe''dx =
e*
+ C
jsinxdx
= -cosx + C
—dx =
tanx + C
•'cos X
—dx
= -cotx + C
•"sin X
7.
Ne'u
\fiu)du
= Fiu)
+
C va
M
=
u(x)
la ham sd cd dao ham lien tuc thi

jfiuix))u'ix)dx
= Fiuix))
+
C.
8. Neu hai ham sd u
= uix)va.v
- vix) cd dao ham lien tuc tren
AT
thi
[u(x)v'(x)dx = u(x)v(x)- [u'(x)v(x)dx; iudv = uv -
wdu
HOAT
DONG 7
M9T
SO
C^a
HOI
TR^C
NGHIEM ON
T6P
B^l
1
Cdu
L
Cho ham sd y
=
x Hay dien diing sai vao cac
cau
sau
(a) Ham so

ludn
cd nguyen ham.
(b) Ham sd chi cd mdt nguyen ham.
(c) Ham so chi cd nguyen ham la
— x
4
(d) Ham sd cd vd sd nguyen ham dang
—
x + C.
4
Trd
Idi.
a
D
b
S
c
S
d
D
D
D
D
D
17
sau
Cdu
2.
Cho ham
sd y

=
Vx Hay
dien diing
sai
vao
cac
cau
(a)
Ham sd
ludn
cd
nguyen ham.
Q
(b) Ham sd chi cd mdt nguyen ham. [J
(c) Ham sd chi cd nguyen ham la
—
x
^
(d) Ham sd cd vd sd nguyen ham dang
—
x
^
+ C.
Trd
Idi.
D
D
a
D
b

s
c
S
d
D
Cdu
3.
Cho ham
sd y
=
x +
cosx.
Hay
dien diing
sai vao cac cau sau
(a)
Ham sd
ludn
cd
nguyen
ham.
(b)
Ham sd
chi
cd mdt
nguyen ham.
1
7
(c)
Ham

sd
chi
cd
nguyen
ham
la
—
x
+
sin
x.
(d)
Ham
sd cd
vd
sd nguyen
ham
dang
.—x^
+
sin
x
+ C.
Trd
Idi.
a
D
b
S
c

S
d
D
Cdu
4. Ham
sd nao sau
day cd nguyen ham
la
2x
(a)y=x'+2
;
(c)
y = 2
;
Trd
led.
(c).
(b)y=2x;
(d)y=
VST.
D
D
D
D
18
Cdu 5. Ham sd nao sau day cd nguyen ham la Vx
(a)y= y = ^^
; (b) y
= -x2
;

2Vx
3
(c)y =
x2;
(d)y=
X
Trd
Idi.
(a).
Cdu 6. Ham sd nao sau day cd nguyen ham la - cos 2x
(a) y = sin2x ; (b) y
=
—sin2x;
(c) y = -sin2x;
(d)y=cos2x.
Trd
Idi.
(b).
Cdu 7. Ham sd nao sau day cd nguyen ham la cos 2x
(a) y
= sin2x
; (b) y
=—sin2x;
(c)y = -sin2x; (d)y=sin2x.
Trd
Idi.
(b).
Cdu
8. Ham so nao sau day cd nguyen ham la sin2x
(a) y

=
sin2x ; (b) y
=
—cos2x;
2
(c) y = -sin2x; (d)y=sin2x.
Trd
Idi.
(b).
Cdu 9. Ham so nao sau day cd nguyen ham la
e"
(a)y =
e'';
(b)y=^e2'';
(c)y
=
lnx;
(d)y=e'"''
Trd
Idi.
(a).
Cdu 10. Ham so nao sau day cd nguyen ham la
In x
(a)y
=
lnx;
(b)y=-;
(c)y = -lnx;
(d)y=e'"''
X

Trd
Idi.
(b).
19
HOAT DONG
8
naCTNG
D^N
Bfil T6P S<iCH GlfiO KHOfi
Bai 1. Hudng ddn. Dua vao dinh nghia nguyen ham.
a) e
^
va -e la nguyen ham
ciia
nhau.
HS tu
tinh
dao ham cua mdi ham sd tren de chiing minh.
b) Lam tuong tu cau a.
2
sin
X
la mdt nguyen ham ciia
sin2x.
c) Lam tuong tu cau a.
4^
e^
la mdt nguyen ham cua 1
X)
Bai 2. Hudng ddn. Su dung cac tinh chat

ciia
nguyen ham.
cau
a. Chia
tii cho
miu, sau dd
sii
dung tinh chat ciia nguyen ham ciia ham sd
y = x"
5 7 2
Ddp sd.
— x3
+—x^
+7;X^
+C.
5 7 2
cau
b. Ddp so
.
2''
+
In
2 - 1
+ C.
e''an2-l)
cau
c. Su dung cong thiic lugng giac va nguyen ham ciia ham sd lugng giac.
Ddp sd. -2cot2x + C.
cau
d. Sii dung cdng thiic lugng giac va nguyen ham cua ham sd lugng giac.

Ddp sd.
1 1
cos8x
+
cos2x
+ C.
cau
e.
Sir
dung cong thiic lugng giac va nguyen ham cua ham sd lugng giac.
Ddp sd. tanx -x+C.
cau
g. Dat
3
- 2x
= u.
Ddpsd.
e^'^^+C.
2
20
cauh.
Ddp sd.
— In
1 1
(1 + x)(l - 2x)
~
3
1 + X
/
1

• +
1 +
X
1 - 2x
l-2x
+ C.
Bai 3. Hudng ddn. Su dung cac tinh chat ciia nguyen ham.
cau a. Dat u = 1- x
Ddp sd.

(1-x)
10
10
-
+ C.
cau
b. Dat u = 1 +
x'
5
Ddpsd -(l +
x^)2+c
cau
c.
Dat
t
=
cos
X
1
Ddp sd.

—
cos x
+
C
4
cau
d. Dat t = cos x
-1
-
+
C
Ddp sd.
\
+
e'
Bai 4. Hudng ddn. Sii dung cac tinh chat
ciia
nguyen ham.
Cau a. Ap dung tinh nguyen ham tirng phan : u = In(l + x), dt; = xdx.
Ddp sd
\ix^
- l)ln(l + x) -
jx^
+
I
+ C
2
X
Cau b.
u

=
X
+ 2x - 1,
du
=
e
dx
Ddp sd
e""
(x^
- 1) + C.
cau
c.u=x,dv
- sin(2x + l)dx.
X 1
Ddp sd. -— cos(2x + 1) +
—
sin(2x + 1) +
C
cau
d. Dat
u
= 1 -
X,
dy
= cosxdx.
Ddp sd.
(1
- x) sin x - cos x + C.
21

§2.
Tich phan
(tiet 6, 7, 8, 9,
lO)
I. MUC TIEU
1.
Kien thiic
HS
nam
dugc ;
Khai niem tich phan la gi?
- Dien tich hinh thang cong ?
- Dinh nghia tich phan.
• Cac tfnh chat cua tich phan.
• Cac phuong phap tinh tich phan
- Phuong phap ddi bien sd.
- Phuong phap nguyen ham tiing
phSn.
Mdi quan he giiia tich phan va nguyen ham.
2.
KT
nang
van
dung thanh thao cac tfnh chat ciia tich phan.
Tfnh dugc tfch phan bang phuong phap ddi bien sd, thanh thao trong viec
ddi bien
sd.
Tinh dugc tfch phan nhd phuong phap tfch phan
tijrng
phin.

3.
Thai do
Tu giac, tfch
cue
trong hgc tap.
Biet phan biet rd cac khai niem
co
ban va
van
dung trong tiing trudng
hgp cu
th^.
Tu duy cac va'n de ciia toan hgc mdt
each
Idgic va he thdng.
H.
CHUAN BI CUA GV VA HS
1.
Chuan bj cua GV
Chudn bi cac cau hdi ggi md.
Chudn bi cac
hinh
tir 45 den hinh 50.
22
Chudn bi pha'n mau va mdt sd dd dung khac.
2.
Chuan bi ciia HS
can
dn lai mot sd kien thiic da hgc ve dao ham va dn tap bai
1.

HI.
PHAN PHOI
TH6I
LUONG
Bai nay chia lam 5
tiet:
Tiet 1 : Tit dau den hit mud phdn I.
Tiet 2 : Tiep theo din het muc 2phdn I.
Tiet 3 : Phdn II.
Tii't 4 : Muc 1 phdn III.
Tii't 3 :Muc 2 phdn III.
IV. TIEN TRINH
DAY -
HOC
A. OAT VAN OE
Cau hoi 1
Neu dinh nghia va tinh chdt ciia nguyen ham.
Neu nhiing van de co ban cua phuong phap ddi bie'n sd va phuong phap
tinh nguyen ham timg phdn.
Cau hdi 2
Tinh nguyen ham ciia cac ham sd sau day:
a)y =
x^-3x
+ 3; b)y =
x.e''
Cau hdi 3
Tim
nguyen ham ciia cac ham sd sau day:
a) y
=

sinx + xcosx. b) y =
xlnx
B. BAI Mdl
I - KHAI NIEM TICH PHAN
HOAT DONG
1
1.
Dien tich hinh thang cong
23