Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

yrelhan4

  • 2 years ago

(1 - x^3)^n integration. limits 0 to 1 ??

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

    try trig sub x^3 = sin^2u

  2. yrelhan4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hmm.. i'll try it once and get back to you..

  3. hartnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    if that doesn't work, do u= 1-x^3

  4. yrelhan4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    how ould that help? @hartnn

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

    du = -3x^2 dx du = - 3(1-u)^(2/3)dx du/[- 3(1-u)^(2/3)] = dx just trying.......

  6. timo86m
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    intigrate with respect to x or n?

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

    |dw:1356588801737:dw|

  8. yrelhan4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @timo86m x

  9. timo86m
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    -x^3/ln(1-x^3) With respect to n

  10. yrelhan4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @experimentX yes i did the same. i think i got it now.. thank you..

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

    this should end up around beta function http://en.wikipedia.org/wiki/Beta_function#Properties

  12. hartnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    is this from Gamma Function ?

  13. timo86m
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[2/9\,{\frac {\Gamma \left( n+1 \right) \pi \,\sqrt {3}}{\Gamma \left( 2/3 \right) \Gamma \left( n+4/3 \right) }} \] gamma

  14. hartnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    because it gets the form u^n (1-u)^n

  15. hartnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    u^n (1-u)^m

  16. timo86m
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh and i used maple got no idea how to do it :P

  17. hartnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    http://www.wolframalpha.com/input/?i=integrate+%281-x%5E3%29%5En+dx+from+0+to+1

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

    \[ \frac{1}{3} \beta(2(n+1), 4/3)) = \]

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

    Umm, can binomial theorem help with this?

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

    \[ \Large (a+b)^n = \sum_{k=0}^{n}\binom{n}{k}a^{n-k}b^{k} \]We let \(a = 1\) and \(b = -x^3\)?

  21. yrelhan4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    can anybody integrate 2/3 [(1-t^2) / (t)^1/3] dt.. from 0 to 1.. i reached till here..

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

    Like what about:\[ \Large \int_0^1\sum_{k=0}^{n}\binom{n}{k}(-x^3)^{k}dx \]

  23. hartnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    how u got that ?

  24. yrelhan4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @wio no idea about it.. its a grade 12 level question.. lol..

  25. yrelhan4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @experimentX 's method..

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

    that's a good strategy!!

  27. timo86m
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    infinity to 2/3 [(1-t^2) / (t)^1/3]

  28. hartnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    i don't think this can be solved without beta functions, did u go to wiki link of beta function ?

  29. yrelhan4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    http://www.wolframalpha.com/input/?i=integrate+%5B%281-t%5E2%29+%2F+%28t%29%5E1%2F3%5D+dt+from+0+to+1 i am talking about this..

  30. yrelhan4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @hartnn hmm.. i gotta read beta function once..

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

    http://www.wolframalpha.com/input/?i=integrate+%5B%281-t%5E2%29+%2F+%28t%29%5E1%2F3%5D+dt

  32. hartnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    thats easy to integrate just seperate the denominator.

  33. hartnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    t^(-1/3) - t^(-5/3)

  34. yrelhan4
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i missed the n.. i think i gota read the beta/gamma function once.. thank you everyone..

  35. hartnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yup, whether u put, u=1-x^3 or x^3 = sin^2 u you'll end up with one of the form of beta function.

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

    for the last one \[ \frac 1 3 \times 2 \int_0^{\pi \over 2} \cos^{2(n+1) - 1}(x) \sin ^{\frac 4 3 - 1 }(x) dx = \frac 13 \beta (n+1, \frac 23 ) = \frac 13 \frac{\Gamma(n+1) \Gamma(2/3)}{\Gamma(n+4/3) } \]

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

    something went wrong

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

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

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.