Page 53 - DMTH202_BASIC_MATHEMATICS_II

Basic Mathematics-II

Notes
3
2
x
2.  (2x  5 )dx
1
2
f ( )  2x  5 ,a  1,b  3andnh  b a  3 1  2
x
x


f ( )  f (1) 7

a
2



)
( f a h  f (1 h  2(1 h )  5(1 h )
)



 2(1 2h h 2 ) 5h  7 9h  2h 2

2
h
h
h
h


( f a  2 )  f (1 2 )  2(1 2 )  5(1 2 )

2
2
 2(1 4h  2 h 2 ) 5 10h   2.9h  2 .2h 2



7
:
:
2
n

( f a n  1 )  f (1 n  1 )  2(1   1 )  5(1   1 )
h
n
h
h

h
2

 2(1 2(n  1)h  (n  1) h 2 ) 5 5(n 1)h


2

 7 (n  1).9h  (n  1) .2h 2
b
h
a
f
f

h
)
)
x
 f ( )dx  lim [ ( )  ( f a h  ( f a h  ( f a  2 (a  3 )

0
h
Now a
  ( f a n  1 )]
h

3
2

h


f
  (2x  5 ) lim [ (1) f (1 h ) f (1 2 ) f (1 3 )

h


x

h
1 h  0
   ( f a n 1 )]
h

2
h
 lim [7 7 9h 2h  2 7 2.9h 2 .2h  2 7 3.9h
h  0
2
2
2
 3 .2h    7  (n 1).9h (n 1) .2h 2 ]

h
 lim [7n 9 (1 2 3   (n 1))
h
h  0
 ( n n  1) 2 (n n  1)(2n  1) 
 lim h 7n 9h  2h
h  0   2 6  
 2 


 lim h 14 9(2 h ) (2 h )(4 h ) [ nh 2]

h  0   3  
16 112
 14 18 
3 3
4
2
3.  (2x  3x  1)dx
2
2
x
f ( ) 2x  3x 1,a  2,b  4and nh  b a  4 2  2



f ( )  f (2) 15
a



)
( f a h  f (2 h ) 2(2  2 ) h  3(2  h ) 1






 2(4 4h h 2 ) 6 3h  1 15 11h  2h 2


2
h
h
h
h





( f a 2 )  f (2 2 ) 2(2 2 )  3(2 2 ) 1
2


 2(1 8h  2 h 2 ) 6 6h  1

2
 15 2.11h  2 .2h 2

2

h

( f a 3 )  f (2 3 ) 2(2 3 ) 3(2 3 ) 1
h

h



h
2
2



 2(4 12h  3 h 2 ) 6 9h  1 15 3.11h  3 .2 h 2


:
:
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