1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Interval with the leingth of 3

  1. Aug 28, 2004 #1
    Draw the function (I can do that) and deside an interval with the leingth of 3, there by f illustrates on an interval in the leingh of 25/4. (how??)

    (hope you can read it, I am from Denmark, so i'll try)
  2. jcsd
  3. Aug 28, 2004 #2
    I'm afraid I don't understand your question. f illustrates an interval? Maybe you could post the question in Danish instead.
    Last edited: Aug 28, 2004
  4. Aug 28, 2004 #3


    User Avatar
    Science Advisor

    You seem to be asking for an interval [a, a+3] (so that the interval has length 3) such that the length of the arc y= x2- 2x+ 2 is 25/4.

    Since y= x2- 2x+ 2, y'= 2x- 2 and ds= [tex]\sqrt{y'^2+1}dx[/tex] (if you don't know what that means, either you need to go back and review "arclength" or I've completely misunderstood your question!).

    This is ds= [tex]\sqrt{4x^2-8x+ 5}= \sqrt{4(x- 1)^2+1}[/tex] is 25/4

    To find the arc-length, we need find [tex]\integral_a^{a+3}\sqrt{4(x-1)^2+1}dx[/tex].
    Do that integral (I suggest the substitution u= 2(x-1) followed by a trig substitution) and then determine what a must be so that the arc-length is
  5. Aug 28, 2004 #4


    User Avatar
    Science Advisor

    Another, simpler, possiblity is that you just want an interval from x to x+3 such that the change in y is 25/3. Since y= x2- 2x+ 2= (x-1)2+1, the change in y between x and x+3 is ((x+2)2+ 1)- ((x-1)2+ 1)= x2+ 4x+ 5- x2- 2x+ 1= 2x+ 6= 25/4. Then 2x= 25/4- 6= 1/4 and x= 1/8.
  6. Aug 28, 2004 #5
    I guess if he can undestand post #3, it is probably this one he should solve.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Interval with the leingth of 3
  1. A^3 + b^3 = c^3 (Replies: 54)

  2. Interval notation (Replies: 4)