# 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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Dec 15, 2009

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.

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