Improper integral with variable

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Homework Help Overview

The discussion revolves around evaluating an improper integral involving the function F(t) defined as an integral of the form S((e^(-tx)) sin(2x)/x)dx from 0 to infinity. Participants are exploring the implications of calculating F(0) and the derivative F'(t).

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the calculation of F(0) and consider how to express F'(t) to facilitate finding F(t). There is also a mention of difficulties encountered while integrating F'(t).

Discussion Status

The discussion is active, with participants sharing insights and seeking assistance on specific challenges related to the integration of F'(t). There is an indication of collaborative problem-solving as participants encourage each other to clarify issues.

Contextual Notes

Some participants express uncertainty about the integration process and the handling of the improper integral, suggesting that there may be constraints or assumptions that need to be addressed.

DIrtyPio
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With the help of F:[0-> infinity) F(t)= S( (e^(-tx)) sin(2x)/x )dx
find the S sin(2x)/x dx . The integral goes from 0 to infinity.
 
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Note that they are basically asking you to calculate F(0).
 
And can you think of a way to write a simple expression for F'(t)? Use that to find F(t).
 
Sorry, indeed I figured out how should I find the other integral, but actually I'm having problems integrateing F'(t).
 
Sorry to hear that. Maybe if you show what kind of problems, someone could help.
 

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