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Monotonicity of the midpoint and trapezium estimates for integrals

Published online by Cambridge University Press:  13 October 2021

G. J. O. Jameson
G. J. O. Jameson*
Affiliation:
13 Sandown Road, Lancaster LA1 4LN, e-mail: pgjameson@talktalk.net
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Extract

The ‘midpoint’ approximation to the integral $$\int_0^1 f $$ is

$${M_n}\left( f \right) = {1 \over n}\sum\limits_{r = 1}^n f \left( {{{2r - 1} \over {2n}}} \right)$$
.

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Type
Articles
Information
The Mathematical Gazette , Volume 105 , Issue 564 , November 2021 , pp. 433 - 441
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Copyright
© The Mathematical Association 2021

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References

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Jameson, G. J. O., Two ways to generate monotonic sequences: convexity and ratios, Math. Gaz. 105 (March 2021) pp. 16-2610.1017/mag.2021.4CrossRefGoogle Scholar