Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

onegirl

Determine whether the integral converges or diverges. Find the value of the integral if it converges.

  • 11 months ago
  • 11 months ago

  • This Question is Closed
  1. onegirl
    Best Response
    You've already chosen the best response.
    Medals 1

    • 11 months ago
    1 Attachment
  2. onegirl
    Best Response
    You've already chosen the best response.
    Medals 1

    @Reaper534 can u help?

    • 11 months ago
  3. terenzreignz
    Best Response
    You've already chosen the best response.
    Medals 1

    Let's just focus on the integral first, keeping in mind that... \[\Large \int\limits_1^\infty x^{-\frac43}= \lim_{b\rightarrow\infty}\int\limits_1^bx^{-\frac43}\]

    • 11 months ago
  4. onegirl
    Best Response
    You've already chosen the best response.
    Medals 1

    okay

    • 11 months ago
  5. terenzreignz
    Best Response
    You've already chosen the best response.
    Medals 1

    Well, can you integrate \[\Large \int x ^{-\frac43}=\color{red}?\]

    • 11 months ago
  6. onegirl
    Best Response
    You've already chosen the best response.
    Medals 1

    yes i get -3/3sqrt(x)

    • 11 months ago
  7. terenzreignz
    Best Response
    You've already chosen the best response.
    Medals 1

    This \[\Large \frac{-3}{3\sqrt{x}}\]?

    • 11 months ago
  8. onegirl
    Best Response
    You've already chosen the best response.
    Medals 1

    yes!

    • 11 months ago
  9. terenzreignz
    Best Response
    You've already chosen the best response.
    Medals 1

    Or this \[\Large \frac{-3}{\sqrt[3]x}\]

    • 11 months ago
  10. onegirl
    Best Response
    You've already chosen the best response.
    Medals 1

    the second one

    • 11 months ago
  11. terenzreignz
    Best Response
    You've already chosen the best response.
    Medals 1

    lol... it's cube root, not 3sqrt because \(\Large3\sqrt x\) means something entirely different, ok?

    • 11 months ago
  12. onegirl
    Best Response
    You've already chosen the best response.
    Medals 1

    Okay

    • 11 months ago
  13. terenzreignz
    Best Response
    You've already chosen the best response.
    Medals 1

    Okay, so, we have... \[\Large \int\limits_1^b x^{-\frac43}=\left.\frac{-3}{\sqrt[3]x}\right]_1^b\]

    • 11 months ago
  14. terenzreignz
    Best Response
    You've already chosen the best response.
    Medals 1

    Can you evaluate this bit?

    • 11 months ago
  15. onegirl
    Best Response
    You've already chosen the best response.
    Medals 1

    i think

    • 11 months ago
  16. terenzreignz
    Best Response
    You've already chosen the best response.
    Medals 1

    Well then, what do you get?

    • 11 months ago
  17. onegirl
    Best Response
    You've already chosen the best response.
    Medals 1

    hmm i'm working on it

    • 11 months ago
  18. onegirl
    Best Response
    You've already chosen the best response.
    Medals 1

    eh...i'm getting a wrong answer :/

    • 11 months ago
  19. terenzreignz
    Best Response
    You've already chosen the best response.
    Medals 1

    Fundamental theorem of Calculus? \[\Large \int\limits_a^b f'(x)dx = \left.f(x)\right]_a^b = f(b)-f(a)\]

    • 11 months ago
  20. onegirl
    Best Response
    You've already chosen the best response.
    Medals 1

    ohhhh okay

    • 11 months ago
  21. terenzreignz
    Best Response
    You've already chosen the best response.
    Medals 1

    So... \[\Large \int\limits_1^b x^{-\frac43} \ dx=\left.\frac{-3}{\sqrt[3]x}\right]_1^b=\color{red}?\]

    • 11 months ago
  22. onegirl
    Best Response
    You've already chosen the best response.
    Medals 1

    so i plug in b and 1 into that then subtract?

    • 11 months ago
  23. terenzreignz
    Best Response
    You've already chosen the best response.
    Medals 1

    Yes... but that's not the end yet, just plug in for now, and tell me what you get :)

    • 11 months ago
  24. onegirl
    Best Response
    You've already chosen the best response.
    Medals 1

    okay so -3/3sqrt(b) - -3/3sqrt(1)

    • 11 months ago
  25. terenzreignz
    Best Response
    You've already chosen the best response.
    Medals 1

    I'm assuming by 3sqrt you mean cube root :D Okay, that being the case, you're right :) \[\Large \int\limits_1^b x^{-\frac43}=\frac{-3}{\sqrt[3]b}+\frac3{\sqrt[3]1}= -\frac3{\sqrt[3]b}+3\] Catch me so far?

    • 11 months ago
  26. onegirl
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

    • 11 months ago
  27. terenzreignz
    Best Response
    You've already chosen the best response.
    Medals 1

    Now, we're supposed to take the improper integral to infinity, right? Remember this... \[\Large \int\limits_1^\infty x^{-\frac43} \ dx = \color{red}{\lim_{b\rightarrow\infty}}\int\limits_1^bx^{-\frac43} \ dx\] Now is the time to apply that limit (which we haven't done yet) \[\Large \color{red}{\lim_{b\rightarrow\infty}}\left(-\frac3{\sqrt[3]b}+3\right) \]

    • 11 months ago
  28. onegirl
    Best Response
    You've already chosen the best response.
    Medals 1

    okay

    • 11 months ago
  29. terenzreignz
    Best Response
    You've already chosen the best response.
    Medals 1

    So... evaluating the limit...?

    • 11 months ago
  30. onegirl
    Best Response
    You've already chosen the best response.
    Medals 1

    umm i get 3? :/

    • 11 months ago
  31. terenzreignz
    Best Response
    You've already chosen the best response.
    Medals 1

    That's right!

    • 11 months ago
  32. onegirl
    Best Response
    You've already chosen the best response.
    Medals 1

    ohh okay lol

    • 11 months ago
  33. onegirl
    Best Response
    You've already chosen the best response.
    Medals 1

    so thats the final answer?

    • 11 months ago
  34. terenzreignz
    Best Response
    You've already chosen the best response.
    Medals 1

    Well, you technically have two questions, but since there was an answer, then the integral converges, and it converges to 3 ^.^

    • 11 months ago
  35. onegirl
    Best Response
    You've already chosen the best response.
    Medals 1

    okay thanks

    • 11 months ago
  36. terenzreignz
    Best Response
    You've already chosen the best response.
    Medals 1

    No problem :)

    • 11 months ago
    • Attachments:

See more questions >>>

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.