Solving Divergent Integral: -infinity Correct?

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Homework Help Overview

The discussion revolves around evaluating a divergent integral involving the expression 1/[(t-3)^(4/3)], with the original poster questioning the correctness of arriving at -infinity as a result.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to confirm whether their result of -infinity is correct and if it indicates divergence. Some participants question the implications of the expression being complex for values of t less than 3.

Discussion Status

Participants are exploring the nature of the integral and its divergence. While some affirm the divergence, there are suggestions to reconsider the sign of the result and the implications of the expression's behavior near t = 3.

Contextual Notes

There is a discussion about the expression being complex for t < 3, which may affect the interpretation of the integral's behavior.

n.a.s.h
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Homework Statement


I had to solve the integral...After all my work i got -infinity
3
integral sign 1/ [(t-3)^4/3]
1


Homework Equations





The Attempt at a Solution


-infinity...is this correct? and would this be divergent?
 
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The expression

<br /> \frac{1}{(t - 3)^{4/3}}<br />

is complex for t &lt; 3.
 
Yes, it is divergent.
 
It has a real root for t<3, so that's not a problem. I would check how you got the sign on that -\infty, though.
 

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