Confused at a fairly simple step in an improper integral

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Homework Help Overview

The discussion revolves around a step in evaluating an improper integral, specifically focusing on the manipulation of terms involving limits and powers.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to understand why a term simplifies to 1 instead of remaining as 1^(1-p). Some participants clarify that any number raised to a power of zero is still 1, while others reflect on the nature of common mistakes in mathematical reasoning.

Discussion Status

The discussion is ongoing, with participants exploring the reasoning behind the simplification. Some guidance has been offered regarding the properties of exponents, but no consensus has been reached on the implications of the original poster's confusion.

Contextual Notes

Participants are navigating the nuances of improper integrals and the handling of limits, with an emphasis on understanding the underlying mathematical principles rather than arriving at a definitive solution.

glmrkl
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Homework Statement



http://puu.sh/fYQQj/12819720c6.png
My question is in the attempt at the solution (Number 3)

2. Homework Equations

The Attempt at a Solution


I know how to get to lim t→∞ 1/(1-p) * (t^(1-p) - 1^(1-p)), I'm not sure what to do to get the 1 instead of 1^(1-p) in the above image
 
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glmrkl said:
I'm not sure what to do to get the 1 instead of 1^(1-p) in the above image
I'm not exactly sure which part you're referring to. But 1 to any power (including 1-p) is just 1.
 
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I was referring to the part highlighted in red which is the simplified form after you solve the integral for x=t and x=1. I was wondering why they had just put 1 instead of 11-p

Well, this is embarrassing :(... thanks nonetheless!
 
At least it let's the rest of us feel superior! (Until we make a similar careless mistake.)
 
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