Suppose the integration rule has the form                 (a) Find the values of 1 , 1 , 1 , and 1 that maximize the precision. [Hint: let  = i +  and find ] (b) The error is known to have the form...

Suppose the integration rule has the form

(a) Find the values of

₁,

₁,

₁, and

₁
that maximize the precision. [Hint: let
 =


_i

+
 and find
]

(b) The error is known to have the form

where, as usual,
 is a point somewhere in the interval [

_i
,


_i+1]. Find
.