The formula for local midpoint rule in the interval [ &#x2212;<!-- − -->

Elle Weber 2022-04-07 Answered
The formula for local midpoint rule in the interval [ h 2 ,   h 2 ]
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Answers (2)

Superina0xb4i
Answered 2022-04-08 Author has 17 answers
Step 1
Set
g ( h ) = h / 2 h / 2 f ( x ) d x h f ( 0 )
and compute
g ( 0 ) = 0 g ( h ) = 1 2 ( f ( h / 2 ) + f ( h / 2 ) ) f ( 0 ) g ( 0 ) = 0
etc. to find the Taylor expansion of g.

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Noelle Wright
Answered 2022-04-09 Author has 6 answers
Step 1
Put f ( x ) = f ( 0 ) + x f ( 0 ) + x 2 f ( 0 ) / 2 + . . . so h / 2 h / 2 f ( x ) d x = h f ( 0 ) + h 3 f ( 0 ) / ( 2 3 8 ) + . . . .

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