A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

unimatix

  • one year ago

Prove that both trapezoid rule and Simpson's rule give an estimate within 0.005 of true value of integral?

  • This Question is Closed
  1. unimatix
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Using Maple I've found: trapezoid rule gives 2.432066146 Simpson's rule gives 2.430797145

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

    \[\int\limits_{a}^{b}\frac{ x^2 }{ \sqrt{(1-x^2)(k^2-x^2)} }\] a = 3 b = 5 k = 2

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

    @SolomonZelman @pooja195

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

    Even if someone just has an idea that might be helpful.

  5. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    error bound on simpsons rule

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

    you want to confirm this numerically or you want to prove it using the error bound theorem

  7. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    i think to find error bounds for trapezoidal one

  8. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    take all right end points and all left end points

  9. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    the true value is between those 2 answers

  10. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    if you show that the difference between trap right end points trap left end points method is less than 0.005 then your answer is within 0.005 of the true value

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

    Okay thanks I'll try and see if I can figure out how to do that.

  12. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    I am not completely sure about this argument though

  13. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    it could be possible that both the right end points and the left end points are both greater than the true value, or both less than the true value

  14. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yeah throw that method out of the window, there is a more mathematical way

  15. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    https://www.youtube.com/watch?v=qVXIU6mKank This tells you about simpsons error bound

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

    Hah that's funny I just found that. I don't see one for the Trapezoid rule though :-/

  17. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    isnt simpsons just a higher order trap

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

    I don't really know what that means.

  19. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    simpsons rule is just like beight a bit smarter about the trapezoidal rule

  20. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    it will take the average of the areas of the trapezoids in a smarter way

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

    Okay. So it will be found in a similar way?

  22. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yeah u should understand the pictures of these operations that will make it a lot clearer

  23. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    https://www.youtube.com/watch?v=uc4xJsi99bk

  24. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    ok i see now

  25. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    basically for trapezoidal

  26. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1442549451279:dw|

  27. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1442549479549:dw|

  28. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    we went from line connections to parabollic connections

  29. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    for trap to simpsons

  30. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    u can keep going on in this way

  31. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    like higher order simpsons rule, instead of parabola u can do x^3 , x^4,x^5 curve connections

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

    Okay that makes sense

  33. 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.