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Homework Help: Evaluate the integral H.W

  1. Aug 19, 2008 #1
    1. The problem statement, all variables and given/known data
    ∫arctan 4t dt


    2. Relevant equations
    integration by parts
    ∫u dv= uv- ∫v du


    3. The attempt at a
    u=arctan dv=4tdt
    du=1/x^2+1 v=t/2

    are these correct, the arctan throws me off
     
  2. jcsd
  3. Aug 19, 2008 #2

    rock.freak667

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    [tex]\int arctan(4t) dt[/tex]

    u=arctan(4t)
    dv=dt

    not what you have.
     
  4. Aug 19, 2008 #3
    du=??????
    dv=t
     
  5. Aug 19, 2008 #4
    Whats the derivative of arctan(x)? Use the chain rule for arctan(4t)
     
  6. Aug 20, 2008 #5
    the derivative for arctan x is 1/1+x^2 and the chain makes it look like (4) 4t/1+x^2
     
  7. Aug 20, 2008 #6

    rock.freak667

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    if x=4t

    [tex]\frac{d}{dx}(arctan(x))=\frac{1}{1+x^2}[/tex]

    so get the differential of arctan(4t), you'll need to multiply [itex]\frac{d}{dx}(arctan(x))[/itex] by [itex]\frac{dx}{dt}[/itex]. What does this give you?
     
  8. Aug 20, 2008 #7
    it'll be 4t/1+x^2
     
  9. Aug 20, 2008 #8
    man im confused
     
  10. Aug 20, 2008 #9

    Defennder

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    You're working in t, not x. As said earlier, use the chain rule for this. Let u=4t. d/dt arctan (4t) = du/dt d/du arctan(u). Express everything in t when you're done.
     
  11. Aug 20, 2008 #10

    rock.freak667

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    Let y=arctan(4t).

    Let u=4t.

    So we have y=arctan(u). What is dy/du?What is du/dt?

    EDIT: ahh Defennder, you type fast
     
  12. Aug 21, 2008 #11

    Gib Z

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    I'm pretty damn confused here as well. Half these posts are showing him how to find the derivative when he wants to know the antiderivative lol. I mean sure, its probably more important to know the derivative first, but thats not what he asked for.
     
  13. Aug 21, 2008 #12
    Hint :
    u=arctan(4t), dv=dt

    It'll work. (Just as you integrate log(x)).
     
  14. Aug 21, 2008 #13

    HallsofIvy

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    Surely you understand that "arctan 4t" does NOT mean "arctan" time "4t"! "arctan" without a variable is meaningless.
     
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