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U substitution

  1. May 23, 2012 #1
    1. The problem statement, all variables and given/known data


    Screenshot2012-05-23at81731PMcopy.png

    Screenshot2012-05-23at81731PM.png


    3. The attempt at a solution

    if x2 = u - 1, and if x3 = x2 * x, then x3 should equal (u-1)x, not .5(u-1).

    I'm assuming that they got u.5 because (x2+1).5 = (u-1+1).5 which is the same as u^.5
     
    Last edited: May 23, 2012
  2. jcsd
  3. May 23, 2012 #2
    Wait, what did you get?

    I ended up getting (in terms of u):

    $$\int\frac{1}{2}\sqrt{u}(u-1) du$$
     
    Last edited: May 23, 2012
  4. May 23, 2012 #3
    if [itex]u=x^{2}+1[/itex], then what does [itex]dx[/itex] equal?
     
  5. May 23, 2012 #4
    Ok, I see that .5du but I still believe that

    if x2 = u - 1, and if x3 = x2 * x, then x3 should equal (u-1)x

    so the new answer should be (u-1)x/2 u^.5
     
  6. May 23, 2012 #5
    [itex]dx≠\frac{1}{2}du[/itex]

    Show how you solve for [itex]dx[/itex].

    EDIT: No, I'm sorry. Solve for [itex]du[/itex] if [itex]u=x^{2}+1[/itex].
     
  7. May 23, 2012 #6
    du = 2xdx

    du/2 = xdx
     
  8. May 23, 2012 #7
    Yes. So then how can you write [itex]x^{3}dx=x^{2}*xdx[/itex]?
     
  9. May 23, 2012 #8
    Ok, I get it now, sort of
     
  10. May 23, 2012 #9
    Don't hold back if you still need help. But just make sure your questions are specific.
     
  11. May 23, 2012 #10
    I think I get it, we'll see if I can apply this technique to future problems, but for now I'm moving on. Thank you for your concern and helping me out.
     
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