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Improper Integral question.

  1. Mar 10, 2012 #1
    1. The problem statement, all variables and given/known data


    Consider the function f(x)=1/(x^p).

    When p>1, the integral of 1/(x^p) from 1 to infinity converges.


    i) For what values of p does the integral of 1/(x^p) from 0 to 1 converge? (0<p<infinity, p does not equal 1).

    ii) Confirm the answer by re-writing the integral of 1/(x^p) from 0 to 1 in terms of area and an integral in terms of y. Comment on any symmetry/asymmetry that this relation demonstrates).
    2. Relevant equations



    3. The attempt at a solution
    i) The integral of 1/(x^p) from 0 to 1 is ((1^(-p+1))/(-p+1))-((0^(-p+1))/(-p+1))
    When p>1, then 0 will have a negative power and the integral will diverge. Therefore the integral converges for 0<p<1.

    ii) I have no clue how to do this part since I don't really understand what the question is asking when it says rewrite the integral in terms of area since the integral itself is about evaluating area. And I don't get the part where it asks to comment on symmetry.

    PLEASE HELP!!!!!!
     
  2. jcsd
  3. Mar 10, 2012 #2
    I think they want you to integrate with respect to y instead of x.
     
  4. Mar 10, 2012 #3
    yeah it says rewrite the integral in terms of y and i had no problem getting that part. the part i didn't get is they ask me to rewrite the integral in terms of area...wtf does that even mean? when you take the definite integral that itself represents area doesn't it??
     
  5. Mar 10, 2012 #4
    Hmm, I have no idea what 'in terms of area' means. Sorry. Ignore? =D
     
    Last edited: Mar 10, 2012
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