What is an example of a definite integral satisfying this property?

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Discussion Overview

The discussion revolves around finding an example of a definite integral that satisfies a specific property, with a focus on the evaluation of integrals over different intervals. The scope includes mathematical reasoning related to integrals.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant requests an example of a definite integral that satisfies a certain property.
  • Another participant provides an example involving the integral \(\int_1^2 x~dx\) and proposes a comparison with integrals over other intervals.
  • It is noted by a third participant that the property holds true for any integral as long as the integrand is integrable over the specified intervals.

Areas of Agreement / Disagreement

Participants do not reach a consensus on a specific example of a definite integral, and the discussion includes multiple perspectives on the property of integrals.

Contextual Notes

The discussion does not clarify the specific property being referenced, and there are assumptions about the integrability of the function over the mentioned intervals.

zorro
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Can somebody give me an example of a definite integral satisfying this property? :

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[tex]\int_1^2 x~dx = 3/2[/tex]
Let c1 = -1, and c2 = -2

Compare the first integral with
[tex]\int_1^{-1} x~dx + \int_{-1}^{-2} x~dx + \int_{-2}^{2} x~dx[/tex]

What do you get?
 
That's true for any integral as long as the integrand is integrable over all those intervals!
 
Thanks!
 

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