Page 41 - DMTH202_BASIC_MATHEMATICS_II

Basic Mathematics-II

Notes
Example:


1
 tan x dx
Set
-1
f = tan x; dg = dx
Deduce

dx
df  ;g  x

1 x 2
Get

x
1
1
1
 tan x dx  1.tan x dx  tan x  
x


1  x 2
1 d (x 2 )
1
x
 tan x  
2 1  x 2
1
1
2
x
 tan x  In (1+ )
x
2
Example:
2x
 xe dx
Set
2x
f = x; dg = e dx
Deduce
e 2x
df  dx ; g 
2
Get
xe 2x e 2x
2x
2n
 xe dx  . x e dx   
2 2
2x x 1 

 e   
 2 4 
Example:
n
 sec x dx

n
Let G(n) = sec x dx

Set
2

f  sec n 2 x  cos 2 n ; x dg  sec x dx

36 LOVELY PROFESSIONAL UNIVERSITY