Math teachers, can you help me out with this calculus question?

Discussion in 'Secondary Education' started by Peachyness, Dec 15, 2009.

  1. Peachyness

    Peachyness Virtuoso

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    [​IMG]
     
  2.  
  3. Peachyness

    Peachyness Virtuoso

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    okay, that didn't come out well.

    So, it's

    x(x+3)^(1/2)dx

    I know you need to do the u substitution.

    so, u=x+3, but du=dx, right? So, what do I do with the x in front of the (x+3)??
     
  4. Aliceacc

    Aliceacc Multitudinous

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    It'a a little hard to read; are you integratng (x+3) to the one half??

    If so, isn't it (x+3) to the 3/2, times 2/3?? I think that, as long as it's one x to the first, it's pretty straight forward.

    That said, I haven't touched calc since 2000, so check my work!
     
  5. Aliceacc

    Aliceacc Multitudinous

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    Sorry Peachy, I misread the question and now have a feverish child in my lap as I type; I'm of no help to you tonight!
     
  6. mmswm

    mmswm Moderator

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    If u=x + 3, then x = u-3, right? You can back substitute and get

    (u -3)u^1/2, then multiply though to get u^3/2 -3u^1/2, which you can easily integrate with the power rule.
     
  7. Peachyness

    Peachyness Virtuoso

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    Let's try this again:
    [​IMG][​IMG]
     
  8. mmswm

    mmswm Moderator

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    Didn't work. :D Did you understand what I typed. Math characters are so hard to type on this forum..
     
  9. Peachyness

    Peachyness Virtuoso

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    you must have posted when I was trying to get this to work. Someone posted a thread on how to do this but, I can't get it to work.... oh well. OKay, I'm going to work out the problem based on what you wrote and see if I can "get it". Thanks!
     
  10. Peachyness

    Peachyness Virtuoso

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    OOOOOOOOOOOOOOOOOOOOOOOOHHHHHHHH, I got it! Thanks!!!
     
  11. mmswm

    mmswm Moderator

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    You're welcome. Don't forget that the solution to most of these 'tricky" problems is usually some sort of simple manipulation. Students get so caught up in the problem being "hard" that they forget to look at the simple things.
     
  12. Peachyness

    Peachyness Virtuoso

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    Yeah, no kidding! Man, that really was so simple, and yet I spent so long staring at that problem.... tsk tsk... thanks! :D
     
  13. Aliceacc

    Aliceacc Multitudinous

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    Sorry I was of no help; I had to strip a bed and get Julia all settled.
     
  14. Peachyness

    Peachyness Virtuoso

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    Oh, Alice, that is all right! I know you're a super busy mom. :)
     
  15. TeacherGroupie

    TeacherGroupie Moderator

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    Peachy, if you haven't got one, you might want copies of either of these:

    Calculus for Cats, by Amdahl and Loats
    Misteaks, and How to Find Them Before the Teacher Does, 3d ed., by Barry Cipra
     
  16. Teaching_101

    Teaching_101 Companion

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    :eek:

    Are you sure you just spoke English?
     
  17. HMM

    HMM Cohort

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    [​IMG]

    Code:
    http://latex.codecogs.com/gif.latex?\int{x(x+3)^{1/2}}dx
     
  18. HMM

    HMM Cohort

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    You can also use integration by parts (if you know how to do that)...though what mmswm did will work just fine.
     
  19. mmswm

    mmswm Moderator

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    I thought about using parts, but it was easier to substitute...at least is was easier to explain on this forum that way. I find that there's rarely only one way to attack a problem. The other reason I went with the way I did is because I wasn't sure what course the OP is taking. I know we didnt' introduce by parts unti Calc2, though there was some simple integration at the end of calc1.
     
  20. HMM

    HMM Cohort

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    I'm betting that the OP has not done integration by parts (based on the type of question asked), but I thought I'd throw out the idea anyway.
     
  21. HMM

    HMM Cohort

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    I thought about going through a power series solution, but then figured that might be a little overkill :p
     
  22. mmswm

    mmswm Moderator

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    :D Remember, we want people to LIKE math. Overwhelming people usually isn't the best way to do that :lol:
     
  23. TeacherGroupie

    TeacherGroupie Moderator

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    (agreeably)

    One can do worse, mm, than to paraphrase E.B. White's remark on William Strunk's goal in writing The Elements of Style:

    "Will felt that the reader/math student was in serious trouble most of the time, floundering in a swamp, and that it was the duty of anyone attempting to write English/teach math to drain this swamp quickly and get the reader/student up on dry ground or at least to throw a rope.”
     
  24. HMM

    HMM Cohort

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    But that is the kind of stuff that made me like math :)
     
  25. mmswm

    mmswm Moderator

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    Yeah, it was linear algebra that did it for me, but, most people would consider too much information frightening.
     
  26. Muttling

    Muttling Devotee

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    Bob the farmer has a 20 by 50 field. What is the area of his field?




    Simple........f(x) = 20 and then integrate f(y) = 20dY from 0 to 50.



    What's not fun about that?






    [​IMG]
     
  27. HMM

    HMM Cohort

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    [​IMG]
     
  28. CindyBlue

    CindyBlue Cohort

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    OK, since no one has posted an answer yet... (grrr!)
    Is it ((2(x+3)^(5/2))/5)-(x+3)^(3/2) ???
    Help me, I'm rusty!
     
  29. mmswm

    mmswm Moderator

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    Almost, but not quite. The last term should be -((x+3)^(3/2))/2
     
  30. HMM

    HMM Cohort

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    I think it should be [​IMG]

    also don't forget your arbitrary constant
     
  31. mmswm

    mmswm Moderator

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    You're right. I haven't been to sleep since 5pm yesterday (it's 7pm now). Serves me right to try to do mental math, while watching mythbusters with my boys and eating chocolate chip cookie dough and surfing the net...all at the same time. Particularly when I'm this tired.
     
  32. HMM

    HMM Cohort

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    [​IMG]
     
  33. mmswm

    mmswm Moderator

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    I need to bookmark that link.
     
  34. HMM

    HMM Cohort

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    yes...it is very nice!
     
  35. mmswm

    mmswm Moderator

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    Drat. It's not a link. It's code. Is there a site that provides the code where one could cut and paste?
     
  36. HMM

    HMM Cohort

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    here is a pdf with a lot of [​IMG] commands
     
  37. TeacherGroupie

    TeacherGroupie Moderator

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    Which presupposes that one has LaTEX on one's computer, yes?
     
  38. HMM

    HMM Cohort

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    No

    Just type in the LaTeX command after

    Code:
    http://latex.codecogs.com/gif.latex?
    Just like

    Code:
    http://latex.codecogs.com/gif.latex?\int{x}dx
    then display as an image...

    [​IMG]
     
  39. TeacherGroupie

    TeacherGroupie Moderator

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    What, like in a regular ol' browser window??
     
  40. HMM

    HMM Cohort

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  41. mmswm

    mmswm Moderator

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    http://latex.codecogs.com/gif.latex?/int{x}dx
     

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