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Definite integration by U subsitution

  1. Nov 30, 2012 #1
    1. The problem statement, all variables and given/known data
    4
    ∫√(t)(10+t)(dt)
    1

    note, only the t is under the square root.
    2. Relevant equations



    3. The attempt at a solution
    Ok. I have to solve this integration problem by U substitution.
    To start, I am not entirely sure what to even set U equal to. I let it equal the number under the square root.

    So,

    U=t
    Du=dx

    But where do i go after this?
     
  2. jcsd
  3. Nov 30, 2012 #2

    Zondrina

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    Homework Helper

    Hey there, welcome to PF.

    Your substitution is wrong, and your derivative as well. You should've gotten u = t so du = dt.

    That will still be wrong though.

    Try the substitution u = [itex]\sqrt{t}[/itex].
     
  4. Nov 30, 2012 #3
    ok. If i set U=√t and Du=dt, where do i go from there? the du=dx was a typo.
     
  5. Nov 30, 2012 #4

    haruspex

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    No, if u=√t du will not equal dt. For the purposes of figuring out the substitution for dt it will be more helpful to write the substitution as u2=t. What does that give when you differentiate?
     
  6. Nov 30, 2012 #5
    derivative of u^2=t is 2u=1?
     
  7. Nov 30, 2012 #6
    If somebody could just do the entire thing via U substitution, that would be great. Then I can see how you did it. I'll be refreshing this page every few minutes.
     
  8. Nov 30, 2012 #7

    Mark44

    Staff: Mentor

    That's clear from the parentheses you have.
    This is NEVER a good substitution, since all you're doing is changing to a different letter. Also, the second line should be du = dt, not du = dx.
     
  9. Nov 30, 2012 #8

    Mark44

    Staff: Mentor

    Do you have to use a substitution?

    If not, rewrite the integrand this way:
    √(t) (10 + t) = 10√(t) + t√(t) = 10t1/2 + t3/2
     
  10. Nov 30, 2012 #9
    Yeah, this is what i have so far

    U^2=t

    2du=dt
     
  11. Nov 30, 2012 #10
    yes, i would prefer to solve this by u substitution, so i can see how its done.
     
  12. Nov 30, 2012 #11

    Mark44

    Staff: Mentor

    No on two counts. First, you're not taking derivatives - you're getting the differentials of u2 and t.

    Second, the differential of t is dt, not 1.

    Here's how it works for both sides:

    d(u2) = d(u2)/dt * dt = 2u * du
    d(t) = d(t)/dt * dt = 1 * dt

    You're new here, so there's a good chance you haven't looked at the forum rules, even though you said you did when you signed on. Take a look at the rules by following the link, especially the Homework Help section.

    You'll see that we won't do the work for you, but we'll help you do the work by guiding you in the right direction.
     
  13. Nov 30, 2012 #12

    Mark44

    Staff: Mentor

    OK, that's a reasonable reason. Follow the suggestions made by Zondrina and haruspex.
     
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