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

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

1. ### PeachynessVirtuoso

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Dec 15, 2009

$\int_{}^{}x(x+3)^(1/2)dx$

3. ### PeachynessVirtuoso

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Dec 15, 2009

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. ### AliceaccMultitudinous

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Dec 15, 2009

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. ### AliceaccMultitudinous

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Dec 15, 2009

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. ### mmswmModerator

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Dec 15, 2009

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. ### PeachynessVirtuoso

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Dec 15, 2009

Let's try this again:
$latex=\int x\sqrt{x@plus;3}" target="_blank"$$\int x\sqrt{x+3}" title="\int x\sqrt{x+3}$

8. ### mmswmModerator

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Dec 15, 2009

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

9. ### PeachynessVirtuoso

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Dec 15, 2009

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. ### PeachynessVirtuoso

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Dec 15, 2009

OOOOOOOOOOOOOOOOOOOOOOOOHHHHHHHH, I got it! Thanks!!!

11. ### mmswmModerator

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Dec 15, 2009

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. ### PeachynessVirtuoso

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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!

13. ### AliceaccMultitudinous

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Dec 15, 2009

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

14. ### PeachynessVirtuoso

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Dec 15, 2009

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

15. ### TeacherGroupieModerator

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Dec 15, 2009

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_101Companion

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Dec 16, 2009

Are you sure you just spoke English?

17. ### HMMCohort

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Dec 16, 2009

$\int {x(x+3)^{1/2}}dx$

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

18. ### HMMCohort

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Dec 16, 2009

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

19. ### mmswmModerator

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Dec 16, 2009

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. ### HMMCohort

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Dec 16, 2009

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. ### HMMCohort

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Dec 16, 2009

I thought about going through a power series solution, but then figured that might be a little overkill

22. ### mmswmModerator

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Dec 16, 2009

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

23. ### TeacherGroupieModerator

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Dec 16, 2009

(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. ### HMMCohort

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Dec 16, 2009

But that is the kind of stuff that made me like math

25. ### mmswmModerator

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Dec 16, 2009

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

26. ### MuttlingDevotee

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Dec 16, 2009

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?

27. ### HMMCohort

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Dec 16, 2009

$\int_0^{20}\int_0^{50}{1}dydx$

28. ### CindyBlueCohort

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Dec 16, 2009

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. ### mmswmModerator

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Dec 16, 2009

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

30. ### HMMCohort

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Dec 16, 2009

I think it should be $-2(x+3)^{3/2}$

also don't forget your arbitrary constant

31. ### mmswmModerator

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Dec 16, 2009

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. ### HMMCohort

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Dec 16, 2009

$\frac{2}{5}(x+3)^{5/2}-2(x+3)^{3/2}+c$

33. ### mmswmModerator

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Dec 16, 2009

I need to bookmark that link.

34. ### HMMCohort

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Dec 16, 2009

yes...it is very nice!

35. ### mmswmModerator

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Dec 16, 2009

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

36. ### HMMCohort

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Dec 16, 2009

here is a pdf with a lot of $\LaTeX$ commands

37. ### TeacherGroupieModerator

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Dec 16, 2009

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

38. ### HMMCohort

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Dec 16, 2009

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...

$\int{x}dx$

39. ### TeacherGroupieModerator

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Dec 16, 2009

What, like in a regular ol' browser window??

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Dec 16, 2009

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