A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Find the length of the curve x=1+9t^2, y=3+6t^3, (0<x<6) PLEASE HELP

  • This Question is Closed
  1. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    hey

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

    can u help?

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

    \[\text{ we have to use this } \int\limits_{a(t)}^{b(t)} \sqrt{(x')^2+(y')^2} dt \text{ or try to use } \\ \int\limits_{a(x)}^{b(x)} \sqrt{ 1+(y')^2} dx\]

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

    oh okay great

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

    do you want to try to write y in terms of x?

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

    yes please

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

    i'm asking that because if we try to write the x limits in terms of t limits we will end up with 4 numbers 2 of them being imaginary

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

    this question is a tad weird for me it is 0<x<6 right?

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

    yea it says Find the length of the curve X=1+9t^2, and y+3+6t^3 (0 <t<6)

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

    that should clarify

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

    oh that makes the problem tons easier you said 0<x<6

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

    yeah sorry

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

    then just use that one parametric formula I gave you

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

    \[\int\limits\limits_{0}^{6}\sqrt{((1+9t^2)')^2+((3+6t^3)')^2} dt\]

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

    i did but my answer wasn't right can u help me check the final answer again?

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

    ok we can check you work what did you get for (1+9t^2)'? and for (3+6t^3)'?

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

    i got 461 for the final answer, but know thats wrong what did u get?

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

    ok but what did you get for the derivatives of those two expressions I asked you above

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

    i did but just wanted to check my final answer first

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

    is there anyway you can tell me what you got for the derivative of (1+9t^2) and (3+6t^3)

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

    did you want me to check your problem?

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

    In order for me to do that I need to see where you went wrong if anywhere

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

    yes i wanted to review the retriceer first then go over questions if possible

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

    18t and 18t^2 is the detractive

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

    i just like to see once i have the answer if i can work back and see my error it helps my learning

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

    great! now inputting those in we get: \[\int\limits_{0}^{6}\sqrt{(18t)^2+(18t^2)^2} dt \\ \sqrt{18^2} \int\limits_0^6\sqrt{t^2+t^4} dt \\ 18 \int\limits_0^6 \sqrt{t^2+t^4} dt\] did you get to this part?

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

    yes

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

    then do i solve from there?? because i got 29200?

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

    notice both terms in the sqrt( ) have a t^2 in common \[\text{ since } t>0 \text{ then we can write }\\ 18 \int\limits_0^6 \sqrt{t^2} \sqrt{1+t^2} dt \\ \\ 18 \int\limits_0^6 t \sqrt{1+t^2} dt \\ \text{ now use substituion }\]

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

    let u=1+t^2

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

    i have to go soon because my battery is about to die, could you share the answer?

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

    is mine right?

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

    please let me know mat 1%

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

    I haven't done the problem. I was hoping we could do it together. If u=1+t^2 then du/dt=?

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

    do you know power rule?

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

    constant rule says (1)'=0 power rule says (t^2)=?

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

    use wolframalpha if you just want answers

  38. 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.