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Summary: TRAPEZOIDAL METHOD
ERROR FORMULA
Theorem Let f(x) have two continuous derivatives on
the interval a x b. Then
ET
n (f)
Z b
a
f(x) dx - Tn(f) = -
h2 (b - a)
12
f00 (cn)
for some cn in the interval [a, b].
Later I will say something about the proof of this re-
sult, as it leads to some other useful formulas for the
error.
The above formula says that the error decreases in
a manner that is roughly proportional to h2. Thus
doubling n (and halving h) should cause the error to
decrease by a factor of approximately 4. This is what
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