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

yrelhan4

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

  • one year ago
  • one year ago

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

    try trig sub x^3 = sin^2u

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

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

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

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

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

    how ould that help? @hartnn

    • one year ago
  5. hartnn
    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.......

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

    intigrate with respect to x or n?

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

    |dw:1356588801737:dw|

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

    @timo86m x

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

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

    • one year ago
  10. yrelhan4
    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..

    • one year ago
  11. experimentX
    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

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

    is this from Gamma Function ?

    • one year ago
  13. timo86m
    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

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

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

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

    u^n (1-u)^m

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

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

    • one year ago
  17. hartnn
    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

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

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

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

    Umm, can binomial theorem help with this?

    • one year ago
  20. wio
    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 \(b = -x^3\)?

    • one year ago
  21. yrelhan4
    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..

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

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

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

    how u got that ?

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

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

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

    @experimentX 's method..

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

    that's a good strategy!!

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

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

    • one year ago
  28. hartnn
    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 ?

    • one year ago
  29. yrelhan4
    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..

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

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

    • one year ago
  31. experimentX
    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

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

    thats easy to integrate just seperate the denominator.

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

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

    • one year ago
  34. yrelhan4
    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..

    • one year ago
  35. hartnn
    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.

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

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

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

    something went wrong

    • one year 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.