Confused at a fairly simple step in an improper integral

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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There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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