A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

find out for what value of p the improper integral +∞ ∫ 1/x^p dx converge. 1 tough questions,,,, i need an explaintion :((

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    0?

  2. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    You need to consider specific cases for p. You set the problem up like this\[\lim_{c \rightarrow \infty} \int\limits_{1}^{c}\frac{1}{x^p}dx\]and consider when: 1. p=1 2. p<1 3. p>1 The integral will only converge for p<1, but I'll leave you to have a go at the mathematics. If you need anything else, let me know.

  3. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    We have to set the integral up as above since this is Riemannian integration, which is only defined on intervals not including +/- infinity. Once we integrate, that's when we can use limits to determine the value.

  4. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    THANKS ALOT

  5. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Become a fan :)

  6. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    but that doesnt make sense, i just did the math, it converges only when p>1 ....

  7. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.