Approaching a Definite Integral with Undefined Limits

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Discussion Overview

The discussion revolves around finding the area under a function f in the interval (a,b) when the integral's limits lead to an undefined situation. Participants explore methods for addressing the undefined nature of F(a) as both the numerator and denominator approach zero.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant describes the integral of the function f as F(x) = h(x)/g(x) and notes that both h(x) and g(x) approach zero as x approaches a, leading to an undefined limit.
  • Another participant suggests looking into improper integrals as a potential approach to the problem.
  • A later reply acknowledges the suggestion and expresses gratitude for the input.
  • One participant proposes using L'Hospital's rule, indicating it may be applicable since the situation presents a 0/0 form, and recommends consulting Bender and Orszag for further insights.
  • A subsequent response thanks the participant for the suggestion regarding L'Hospital's rule.

Areas of Agreement / Disagreement

Participants do not reach a consensus on a specific method to resolve the undefined limit, but multiple approaches are suggested, indicating a variety of perspectives on how to tackle the problem.

Contextual Notes

The discussion does not clarify the specific conditions under which L'Hospital's rule or improper integrals would be applicable, nor does it resolve the mathematical steps necessary to approach the problem.

Apteronotus
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I want to find the area under a function f in the interval (a,b).

I've calculated the integral of the function f, and its given by:
\int f(x) dx=F(x)

Now the problem I have is that F(a) is not defined. In particular, F(x)=\frac{h(x)}{g(x)} and
as x \rightarrow a, h(x) \rightarrow 0
and x \rightarrow a, g(x) \rightarrow 0

How would I approach this problem?
 
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Yes of course!
Thank you kindly NME.
 
You can probably use the L'Hospital's rule if everything is good since this is 0/0.
Look up Bender and Orszag maybe.
 
Thanks for the helpful tip prav.
 

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