# Bài tập Tích phân

BA
̀
I TÂ
̣
P TOA
́
N LƠ
́
P 12 Nguyễn Thanh Lam
NGUYÊN HA
̀
M - TI
́
CH PHÂN VA
̀
Ư
́
NG DU
̣
NG
I. NGUYÊN HA
̀
M



( )

 x x dx− +


 

x x dx
x
 
− +
 ÷
 


( )

x x x dx+ +



 
dx
x x
 

 ÷
 



x
dx
x

 
 ÷
 


( ) ( )
 x x x dx+ − +


( )

x x
e e dx




x
x
e
e dx
x

 
+
 ÷
 


( )

x
a x dx+


( )
 
x x
dx+



 x x
dx
x
+ +


( )

 
dx
x +



 xdx−


( )
  x dx+


( )
  x x dx+


 x xdx


 
  

x
x dx
 
+
 ÷
 


( )
 
 x x dx−


( )
 
 x x dx−


( )
 
 x x dx+


 
 
dx
x x



 xdx



 
dx
x x− +



  
dx
x x− +


( )

 x dx+


 xdx


 xdx



x x dx+


 
x x dx+




x
e xdx



 xdx



 xdx



 xdx



 xdx



 xdx



 xdx


x
xe dx


 x
xe dx


x xdx


x xdx


x xdx


 xdx


x xdx



x xdx


  x
dx
x
+




 
x
e xdx



x dx
x +



x
dx
x +

II. TI
́
CH PHÂN
---------------------------------------------------------------------------------------------------------------------------------------------------------
Năm ho
̣
c 2010 - 2011
BA
̀
I TÂ
̣
P TOA
́
N LƠ
́
P 12 Nguyễn Thanh Lam





xdx



e
dx
x



dx
x



 

x dx
x
 
+
 ÷
 



x x
dx
x



  
e
x x
dx
x
+ −



 xdx
π



 xdx
π



 x xdx
π
π



   x xdx
π
π



x x
dx
x
− +
+



 

 

x x
dx
x
− +





x dx
π
π
 

 ÷
 



 
dx
x x+ + −


( )

 x cos x dx
π
π

+


( )

  x cos x dx
π
π



 xdx
π



 xdx
π



 xdx
π



 xdx
π



 x dx−



 x x dx+ −



 x dx
π



  
o
xdx
π



x
xe dx



x
xe dx


( )

 x dx+



xdx
x +



 

x x dx−



 xdx
π



 xdx
π



 xdx
π

---------------------------------------------------------------------------------------------------------------------------------------------------------
Năm ho
̣
c 2010 - 2011
BA
̀
I TÂ
̣
P TOA
́
N LƠ
́
P 12 Nguyễn Thanh Lam


 xdx
π
π




 
x
dx
x
π
+



  x xdx
π
+






x
e xdx
π



 
e
x
dx
x
+





 
x
e xdx
π




 
e
x
dx
x x−



x dx
x +



 

x x dx+



 x xdx
π




 
x
dx
x
π
+



  

x x dx+



 

a
dx
a x−




x a t
=


dx
x−



dx
x−



dx
x−



 

a
a x dx−




x a t
=


 x dx−



 x dx−



 x dx−


 

a
dx
a x+




x a t=


dx
x+



dx
x x+ +



 

x x dx−



dx
x x−


  
π π π
 
= −
 ÷
 


x
dx
x
+




x t=




dx
x
π
π



 
 
  !
  
x t t
t x x
t t

= ⇒ = =
+ +


x
dx
x +



x
dx
x



x
x x
e
dx
e e

+





x
dx
e −



 
 
x
dx
x x
+
+ −

---------------------------------------------------------------------------------------------------------------------------------------------------------
Năm ho
̣
c 2010 - 2011
BA
̀
I TÂ
̣
P TOA
́
N LƠ
́
P 12 Nguyễn Thanh Lam


 
xdx
x x+ +



 
dx
x x
π
π


( )

 
e
x
dx
x
π


( )

 
e
x
dx
x
π



x
xe dx


( )

 x xdx
π


( )

  x xdx
π



x
x e dx



x xdx
π



x xdx
π




x
e xdx
π




x
e xdx
π




e
x xdx




e
xdx




e
xdx


( )

  x x dx−




e
x
dx
x




e
x xdx



x xdx



x xdx




x xdx



x xdx

III. BÂ
́
T ĐĂ
̉
NG THƯ
́
C CU
̉
A TI
́
CHPHÂN
"#

\$%
&
 :


 

 
x
dx
+
≤ ≤



 
  
dx
x

≤ ≤
+



  
x x
dx

≤ ≤



   
dx
x
π
π
π π
≤ ≤


( )


    x x dx

≤ + + − ≤



 
 
xdx
π
π
π π
≤ + ≤



   
dx
x
π
π π
≤ ≤
+


---------------------------------------------------------------------------------------------------------------------------------------------------------
Năm ho
̣
c 2010 - 2011
BA
̀
I TÂ
̣
P TOA
́
N LƠ
́
P 12 Nguyễn Thanh Lam
IV. ÔN TÂ
̣
P VÊ
̀
TI
́
CH PHÂN
'(

+
+
=



π
dx
x
xx
I
'(
dx
x
xx
I

+
=



π
'(
( )

+=



π
xdxxeI
x
'(
dx
x
x
I

+
+
=

'(

 I x xdx
π
=

'(
( )



 
x
I x e x dx
π
= +

'(

=
e
xdxxI


'(
dxxxI

+=



'(

+++

=



dx
xx
x
I
'(
dxxxI

−=



'(

=


π
xdxeI
x
'(

 

I x x dx= +

'(

+

=



π
dx
x
x
I
'(

++
=

xx
dx
I
'(

=
e
dx
x
x
I


'(
dx
x
x
I

+
+
=



'(

+
=



π
dx
x
x
I
'(

=
+
=







π
π
xx
xdxx
J
x
xx
xdx
I
'(

=
e
xdxxI


'(
dxxxI 

=
π
'(
dx
x
xxx
I

+
+++
=




'(
( )

+
=

x
xdx
I

'(

=
e
xx
dx
I


'(

+
=





π
dx
xx
x
I
'(

+
=



π
dx
x
x
I
'(
2
2 2
0
sin 2x
I dx
cos x 4sin x
π
=
+

'(
6
2
dx
I
2x 1 4x 1
=
+ + +

'(
( )
1
2x
0
I x 2 e dx= −

---------------------------------------------------------------------------------------------------------------------------------------------------------
Năm ho
̣
c 2010 - 2011

Generate time = 0.3536810874939 s. Memory usage = 1.94 MB