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cabellos6
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Homework Statement
the integral of 3/x
Homework Equations
The Attempt at a Solution
am i right in saying this is 3lnx
Is the Integral of 3/x Equal to 3lnx?
- Thread starter cabellos6
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Homework Help Overview
The discussion revolves around the integral of the function 3/x, with participants exploring its evaluation and implications, particularly in the context of limits of integration.
Discussion Character
- Exploratory, Conceptual clarification, Mathematical reasoning
Approaches and Questions Raised
- Participants discuss whether the integral can be expressed as 3ln|x| and emphasize the importance of including an arbitrary constant. There is also a shift towards considering the integral with limits of integration, prompting questions about evaluating improper integrals.
Discussion Status
Some participants affirm the expression for the integral while others introduce the concept of improper integrals, indicating a productive exploration of the topic. Multiple interpretations regarding the limits of integration are being examined.
Contextual Notes
There is mention of the need to evaluate the integral as an improper definite integral, which introduces additional considerations regarding the limits approaching zero and infinity.
the integral of 3/x
am i right in saying this is 3lnx
- #2
Kurdt
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Yes you are. Don't forget the arbitrary constant.
- #3
quantumdude
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And don't forget the absolute value bars. It's 3ln|x|+C.
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Kurdt
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Tom Mattson said:
Indeed
Welcome back Tom!
Last edited:
- #5
rxtrejo
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Same question adding Limits of integration b=infinity a=0
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Hootenanny
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Well, what do you think it is?rxtrejo said:
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NJunJie
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rxtrejo - you asking a question?
That would mean substituting the bounded values and find some 'area' within the limits you have given.
That would mean substituting the bounded values and find some 'area' within the limits you have given.
- #8
Mark44
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Not so fast. This is an improper definite integral that requires limits at both endpoints to evaluate.NJunJie said:
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Mark44
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IOW,
3\int_0^{\infty} \frac{dx}{x}<br /> = 3\lim_{a \rightarrow 0_+}\int_a^{1} \frac{dx}{x}~+~ 3\lim_{b \rightarrow \infty}\int_1^{b} \frac{dx}{x}
I chose to split the first integral at 1. Any reasonable value could be used to divide the original interval into two subintervals.
3\int_0^{\infty} \frac{dx}{x}<br /> = 3\lim_{a \rightarrow 0_+}\int_a^{1} \frac{dx}{x}~+~ 3\lim_{b \rightarrow \infty}\int_1^{b} \frac{dx}{x}
I chose to split the first integral at 1. Any reasonable value could be used to divide the original interval into two subintervals.
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