Hostname: page-component-7dd5485656-hw7sx Total loading time: 0 Render date: 2025-10-31T16:44:26.272Z Has data issue: false hasContentIssue false
  • English
  • Français

The Second Mean Value Theorem in the Integral Calculus

Published online by Cambridge University Press:  24 October 2008

A. C. Dixon
A. C. Dixon
Affiliation:
Trinity College
Get access Rights & Permissions [Opens in a new window]

Extract

Hobson has given a proof of this theorem in its fullest generality. The present note gives an alternative for part of Hobson's argument. The theorem may be stated in two forms. If f(x) is a function of x, monotone when a ≤ x ≤ b, and φ(x) is integrable over the same range, then

where a ≤ X ≤ b,

(ii) the same holds with a < X < b except in some trivial cases where f(x) is constant in the open interval a < x < b. The form (ii) is not mentioned by Hobson.

Information

Type
Articles
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 25 , Issue 3 , July 1929 , pp. 282 - 284
Copyright
Copyright © Cambridge Philosophical Society 1929

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

* Proc. Lond. Math. Soc., Ser. 2, Vol. VII, pp. 14–23 (1909).Google Scholar

* For the method of proof of this theorem, see Phil. Trans. Roy. Soc. A, 211, pp. 413–416 (1911).Google Scholar