WebAssign login info Username: hybridtheorygfx Institution: suffolk Pw: Bourd@in123 (case sensitive)

Sol: (1) (a) Given that
2( ) 2 , ( ) 4G x x f x x 
On taking a antiderivative of ( )f x ,
2
2
( ) 4
( ) 4
2
( ) 2
( ) ( )
f x dx x dx
x
f x dx C
f x dx x C
f x dx G x C

 
  
 
   
 
 




So ( )G x is an antiderivative of ( )f x because '( ) ( ) .G x f x for all x
(b) All the antiderivative of f
 2 2 22 4, 2 , 2 4x x x 
(c)
Sol: (2)
 
14 14 1
14
dx dx
x C

 
 
Sol: (3)
4 1
4
3
3
3
2 2
4 1
2
3
2
3
2
3
t
t dt C
t
C
t
C
C
t
 



 
  
  
 
  
 
  
  


Sol: (4)
4
4
4 1
3
3
1 1
3 3
1

3 4 1
1

3 3
1 1

9
dx x dx
x
x
C
x
C
C
x

 


 
  
  
 
  
 
 
   
 
 
Sol:...