Note that
Now using the formula ( 13.3.2) for
Thus, we have,
i.e.
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|
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(13.3.4) |
where
Recall that in the case of linear function, the second forward differences is zero, hence, the Trapezoidal rule gives exact value of the integral if the integrand is a linear function.
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0.0 | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | 1.0 |
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1.00000 | 1.01005 | 1.04081 | 1.09417 | 1.17351 | 1.28402 | 1.43332 | 1.63231 | 1.89648 | 2.2479 | 2.71828 |
and
Thus,