6. Midpoint Rule
Let f be continuous on [a, b].
The Midpoint Rule for approximating
is given by
x
y
a 1
x 2
x bnx…
)(xfy
b
a
dxxf )(
1 2
( )
[ ( ) ( ) ... ( )]
b
na
n
f x dx M
x f x f x f x
b a
x
n
1
1 12 ( ) midpoint of [ , ]i i i i ix x x x x
Where
and