Newton Leibnitz Formula for Evaluating Definite Integrals

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Discussion Overview

The discussion centers around the Newton Leibnitz Formula for evaluating definite integrals, particularly the conditions under which it applies, specifically the requirement for the function f(x) to be continuous on the interval [a, b]. Participants express confusion and seek clarification on this aspect.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions why continuity of f(x) is necessary for applying the Newton Leibnitz Formula, indicating a lack of understanding regarding this condition.
  • Another participant clarifies that the formula applies only if f is continuous on the interval [a, b], emphasizing that the theorem does not address scenarios where f is not continuous.
  • A third participant connects the discussion to the Fundamental Theorem of Calculus, suggesting that it relates to the evaluation of integrals.
  • Several participants provide links to external resources for further reading on the topic, indicating a desire for additional context and understanding.

Areas of Agreement / Disagreement

There is no consensus on the necessity of continuity for the application of the formula, as participants express differing views on its implications and the conditions under which it holds true.

Contextual Notes

The discussion highlights the ambiguity surrounding the implications of the continuity condition in the context of the theorem, with no resolution on how to interpret cases where f is not continuous.

andyrk
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Lately, I have been trying really hard to understand the Newton Leibnitz Formula for evaluating Definite Integrals. It states that-
If f(x) is continuous in [a,b] then \int_a^b f(x) dx = F(b) - F(a).
But one thing that just doesn't make sense to me is that why should f(x) be continuous in [a,b] if we need to apply this formula?
Reply soon!
 
Last edited:
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Anybody there?
 
do you know limit as as sum formula?
 
It doesn't say that. The statement "if a then b" means "if a is true then b is true". It does NOT say anything about what happens if the hypothesis is NOT true.

This theorem says that "if f is continuous on the interval [a, b], then \int_a^b f(t)dt= F(b)- F(a)". It does NOT say anything about what happens if f is NOT continuous, If f is not continuous, then this may or may not be true.
 
please read this-http://www3.ul.ie/~mlc/support/Loughborough%20website/chap15/15_1.pdf
 
read it fully and pay attention to the formula of the area.
 

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