Confused at a fairly simple step in an improper integral

In summary, the conversation is about a question regarding a solution attempt for finding the limit of a function. The person is unsure about using 1 or 1^(1-p) in the simplified form of the solution. The other person points out that 1 to any power is just 1. The initial person realizes their mistake and thanks the other person.
  • #1
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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  • #2
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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  • #3
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!
 
  • #4
At least it let's the rest of us feel superior! (Until we make a similar careless mistake.)
 
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FAQ: Confused at a fairly simple step in an improper integral

1. What is an improper integral?

An improper integral is an integral where one or both of the limits of integration are infinite or the function being integrated has an infinite discontinuity within the interval. In simpler terms, it is an integral that does not have a finite value due to certain conditions.

2. What makes a step in an improper integral confusing?

A step in an improper integral can be confusing because it may involve manipulating and evaluating infinite or undefined values, which can be counterintuitive and require a different approach than a regular integral.

3. How do you know if an integral is improper?

An integral is improper if one or both of the limits of integration are infinite or the function being integrated has an infinite discontinuity within the interval. It can also be improper if the integrand approaches infinity at one or both of the limits of integration.

4. What are some common techniques for solving improper integrals?

Some common techniques for solving improper integrals include using limits of integration, breaking the integral into smaller parts, using substitution, and applying the Comparison Test or the Limit Comparison Test.

5. Can an improper integral have a finite value?

Yes, an improper integral can have a finite value if the improper behavior at the limits of integration can be cancelled out or compensated for by the function being integrated. This can be achieved through techniques such as integration by parts or using a different variable of integration.

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