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

FoolForMath Group Title

Just another cute integral: \[\int |x|^3 \; dx \] and yes this is indefinite ;)

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. Ishaan94 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Hmm \[ \int |x|^2 = \left\{\begin{array}{kcc}\frac{1}{4}\cdot x^4, \quad x>0 \\ 0, \quad x = 0 \\ \frac{-1}{4}x^4, \quad x<0 \end{array}\right.\]Maybe?

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

    I have never seen a indefinite integral represented like this.

    • 2 years ago
  3. Ishaan94 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Me neither but I never had to integrate modulus functions without limits before. It has to be like this, I am quite sure.

    • 2 years ago
  4. shivam_bhalla Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\int\limits_{}^{}|x|^3 dx = \frac{x^3*|x|}{4}+c\] I hope this is right @FoolForMath and congrats on being a new moderator

    • 2 years ago
  5. Ishaan94 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    This can't be right, |x| stays positive but the x^3 can get negative.

    • 2 years ago
  6. Ishaan94 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    I am not sure though. and I can be wrong.

    • 2 years ago
  7. shivam_bhalla Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    For negative x , |x| = -x and therfore integral value would be positive. Though I can be wrong @ this

    • 2 years ago
  8. Ishaan94 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    For negative x, x^3 * |x| = (-x)^3 (-(-x)) = -x^4

    • 2 years ago
  9. Ishaan94 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    What's wrong piece wise representation?

    • 2 years ago
  10. Ishaan94 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    wait... my piece wise is gonna give same result as yours

    • 2 years ago
  11. Ishaan94 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    so, either we are both wrong or right

    • 2 years ago
  12. shivam_bhalla Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\huge \int\limits\limits_{}^{}|x|^3 dx = {sgn(x)}* \frac{x^4}{4}+c\]

    • 2 years ago
  13. Ishaan94 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    and your integral does seems better

    • 2 years ago
  14. Ishaan94 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    ohh yeah

    • 2 years ago
  15. Ishaan94 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    sgn(x) how could i not think about it!?!?! :(

    • 2 years ago
  16. Ishaan94 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    so, there are multiple ways of representing same integral?

    • 2 years ago
  17. Ishaan94 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    because every integral on this page is gonna get you the same result

    • 2 years ago
  18. Ishaan94 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    so, how do you rule out others? and make one right.

    • 2 years ago
  19. shivam_bhalla Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    @Ishaan94 , Is my integral right because substitute -x and check please

    • 2 years ago
  20. Ishaan94 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    -x^4/4 is what we will get. sgn(-x)x^4/4 = -1* x^4/4

    • 2 years ago
  21. shivam_bhalla Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Yes and why is it negative??

    • 2 years ago
  22. shivam_bhalla Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I have confused myself lolol

    • 2 years ago
  23. Ishaan94 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    i am confused myself and blabbering :/

    • 2 years ago
  24. shivam_bhalla Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Same here LOL. However I wolframed it and it is giving my equation. The sgn(x) one. Ditto . ??

    • 2 years ago
  25. shivam_bhalla Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Ok I got it. Taking example always helps

    • 2 years ago
  26. shivam_bhalla Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    In that case how is my first equation wrong , the very first one I mentioned ??

    • 2 years ago
  27. Ishaan94 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    \[\int_{-1}^1 |x|^3 = \int_{-1}^0 -x^3 + \int_{0}^1 x^3 = -(-1/4) + \frac14 = \frac12 \] \[\left[sgn(x) \cdot \frac{x^4}{4}\right]_{-1}^1 = \frac{1}4 + \frac14\]

    • 2 years ago
  28. Ishaan94 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Your first integral was right as well

    • 2 years ago
  29. Ishaan94 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    My piece wise representation is pelletty :/

    • 2 years ago
  30. shivam_bhalla Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Haha. Maths always confuses us even when we have the right answers . :P

    • 2 years ago
  31. Ishaan94 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    yeah hahaha i never had to integrate such indefinite integrals before.

    • 2 years ago
  32. Ishaan94 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Why isn't FoolForMath replying?

    • 2 years ago
  33. shivam_bhalla Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Only 2 people know the answer to your question @Ishaan94 , @FoolForMath and god himself :P

    • 2 years ago
  34. Ishaan94 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    lol

    • 2 years ago
  35. FoolForMath Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Lol, I had the answer but I only figured it out why is it working. Thanks to M.se again ;)

    • 2 years ago
  36. Ishaan94 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    @God

    • 2 years ago
  37. Ishaan94 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    0 fans lol

    • 2 years ago
  38. Ishaan94 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    I beat God! by 455 fans

    • 2 years ago
  39. shivam_bhalla Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    LOLOL

    • 2 years ago
  40. FoolForMath Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    So, the answer is \[ \frac 1 4 |x|^3 \cdot x +C \]

    • 2 years ago
  41. shivam_bhalla Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Does it matter, @FoolForMath the position of modulus on either x^3 or x :P

    • 2 years 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.