Integrating Factor: -g(m/g) and its Derivative

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Homework Help Overview

The discussion revolves around the integration of a function involving the gravitational constant g and its relationship with mass m. Participants are examining the implications of differentiating and integrating these terms in the context of a specific problem.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are questioning how -g transforms into -g(m/g) and discussing the derivative of -g. There is also confusion regarding the integration process and the role of constants in the equations presented.

Discussion Status

The discussion is ongoing, with participants offering insights into the nature of constants in integration and differentiation. Some are attempting to clarify the context and implications of the variables involved, while others are exploring different interpretations of the problem.

Contextual Notes

There is mention of a scanned document that may lack clarity, which could be affecting participants' understanding of the problem setup. The gravitational constant g is noted as a point of confusion, particularly regarding its treatment in integration.

Ry122
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In the following problem how does -g end up becoming -g(m/g)?
Isn't the derivative of -g just (-g^2/2)?
http://users.on.net/~rohanlal/integfact.jpg
 
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I'm having trouble reading the scan, but from what I can tell, the factor of (m/c?) came from integrating the exponential, and g is constant with respect to the variable t. Then again, I don't have any context either.
 
Yes, in this case g is a constant because you are integrating with respect to t. If you were integrating with respect to g (no clue why you would because I strongly suspect that this is the gravitational constant) then everything else would be a constant and you would get -g^2/2.
 
Shouldn't I also have to find the integral of g, which would be gt?
 

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