A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Loser66

  • one year ago

\[J=\int_0^1\sqrt{1-x^4}\] \[K=\int_0^1\sqrt{1+x^4}\] \[L=\int_0^1\sqrt{1-x^8}\] A) J<L<1<K B) J<L<K<1 C) L<J<1<K D) L<J<K<1 E) L<1<J<K please, help.

  • This Question is Closed
  1. theopenstudyowl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    #walframa

  2. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thanks, but no.

  3. MeowLover17
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    lol @theopenstudyowl

  4. theopenstudyowl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Meow...lol

  5. MeowLover17
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    =^-^=

  6. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Please, dont' mess my post

  7. MeowLover17
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @welshfella

  8. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @ganeshie8 any shortest way to find the answer without graphing or calculating?

  9. nincompoop
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    visualise it

  10. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    graphing?

  11. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Ahh graphing looks neat!

  12. nincompoop
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you don't want to "graph" it, so visualize

  13. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    ohk i misread you don't want to graph/evaluate...

  14. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @nincompoop what is difference between graph and visualize?

  15. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    visualize = graphing in ur head

  16. nincompoop
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    GRAPH WOULD INVOLVE YOU ACTUALLY GRAPHING IT, VISUALIZE THAT INVOLVES JUST MENTAL

  17. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Wouldn't \(\sqrt{1-x^{8}}\) have steep climbs and descents than \(\sqrt{1-x^{4}}\) ? I would expect because of the increased steepness in \(\sqrt{1-x^{8}}\) that it's integral would be of greater value. \(\sqrt{1+x^{4}}\) Would never tend towards the x-axis. It should be very similar to \(\sqrt{1-x^{4}}\) But increasing as x increases. So trying to logic it out, I would say J < L < K

  18. nincompoop
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    THERE YOU GO!

  19. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    For \(x\in (0,1)\) do we have \(x^m \lt x^n\) if \(m \gt n\) ?

  20. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    then apply concentrationalizing logic

  21. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Got it. Thanks you all. :)

  22. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    You're welcome :)

  23. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    looks the question boils down to simply putting the given integrands in ascending order

  24. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    When graphing, J >1, and others <1, hence A is a correct answer. But I would like to shorten the time solving it. :)

  25. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    \[x^4 \gt x^8 \implies -x^4 \lt -x^8 \implies 1-x^4\lt 1-x^8 \implies \sqrt{ 1-x^4}\lt \sqrt{ 1-x^8}\]

  26. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yyyyyyyyyyyyyyyes!! that 's good.

  27. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    just from 0 to 1, that's true, right?

  28. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    oh forgot to put that, yes all that is valid only for \(x\in (0,1)\)

  29. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thanks a lot.

  30. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    np sometimes it is hard to see \(x^4 \lt x\) for \(x\in (0,1)\)

  31. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    if we let \(x = 0.9\), we get \(x^4 = 0.9*0.9*0.9*x\) which is clearly less than \(x\)

  32. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    it is less than \(x\) because multiplying anything by a proper fraction always produces a smaller number (0.9 = 9/10 is a proper fraction)

  33. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah, and we know that 1+ whatever >1, hence K>1 , others <1, good interpretation. :)

  34. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    yeah that was easy :)

  35. 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.