How Do You Calculate the Area Under the Curve f(x) = 9/x from 5 to 10?

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Discussion Overview

The discussion revolves around calculating the area under the curve of the function f(x) = 9/x over the interval [5, 10]. Participants explore the relationship between the function and its potential antiderivative, as well as the implications of notation used in the problem statement.

Discussion Character

  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant asks for clarification on whether F(x) = 9/x is intended to represent the function whose area is to be calculated or if it is mistakenly capitalized, implying a derivative relationship.
  • Another participant notes that the notation typically indicates an antiderivative and suggests evaluating F from the specified bounds, though they do not provide a definitive method for doing so.
  • A later post reiterates the need for precision in the relationship between F(x) and f(x), emphasizing the importance of notation in understanding the problem.
  • One participant provides the expression 9ln|x| + c, which may relate to the antiderivative, but the context of its application remains unclear.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the interpretation of F(x) and its relationship to f(x). There are multiple viewpoints regarding the notation and the steps needed to calculate the area under the curve.

Contextual Notes

The discussion highlights potential ambiguities in notation and the assumptions underlying the interpretation of F(x) as an antiderivative. The mathematical steps for evaluating the area remain unresolved.

mathdum
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Find the area of the region under the graph of the function f on the interval [5, 10].
F(x) = 9/x
 
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When you say that F(x) = 9/x, do you mean that F'(x) = f(x) where f(x) is the function whose area under its curve you want to calculate? Or did you mistakenly capitalize "f"?
 
Well, my problem just says F(x). Other problems have F'(x), However, this one does not. Hmm...
 
mathdum said:
Well, my problem just says F(x). Other problems have F'(x), However, this one does not. Hmm...

Usually capitalized notation means that it is the anti-derivative. This means you should evaluate F from the given bounds. Do you know how to do this?
 
mathdum said:
Find the area of the region under the graph of the function f on the interval [5, 10].
F(x) = 9/x
Try to be precise in the relationship between F(x) and f(x).
 
9ln|x| + c
 

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