# first use of geogebra to do a simple integration

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#### DeusAbscondus

##### Active member
Would someone be kind enough to have a glance at my first fumbling steps in using geogebra to solve integration problems?

Thanks.

I'm over the moon, freshly in love with maths, since this morning's class, when we learnt how to use the definite integral.

I have no-one else on the Blue Planet to share this arcane joy with....
so few of my co-species "gets it" when it comes to the aesthetic pleasure of numbers and the virtigenous philosophical buzz attached thereto.

Oh, and any comments on how to improve my latex would be spiffingly good to receive....

Regs,
Deus Abscondus
("Quand nous essayons de nous approchons de lui, il nous fuit avec une fuite eternelle ..... " Now, now, Blaise, what would be another inference just begging to be drawn here?)

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#### Jameson

Staff member
Hi DeusAbscondus,

I'm not familiar with that program but it's great to see your progress through calculus since you joined. Learning integration can be a tricky thing. In my experience often times the theory behind definite integrals is skipped over lightly because the connection between derivatives and integrals makes calculating the latter easier. If you have time I recommend reading up on Riemann sums - using them to approximate the area under a curve and how by using "infinitely" many rectangles the true area can be found.

Anyway, you made this thread in the Latex forum so I'm curious as to what questions you have about Latex? You said you want to improve it, but in what way? Learning more commands, related to integration perhaps?

Congrats again on your progress and I look forward to you posting some tough integrals for me to practice solving!

Jameson

#### DeusAbscondus

##### Active member
Hi DeusAbscondus,

Anyway, you made this thread in the Latex forum so I'm curious as to what questions you have about Latex? You said you want to improve it, but in what way? Learning more commands, related to integration perhaps?

Congrats again on your progress and I look forward to you posting some tough integrals for me to practice solving!

Jameson
Hi Jameson,
I mainly wanted to know that I had the parsing, symbols and math all correct in the sample provided, and that, if I didn't, I could learn where and in what ways to correct, improve or be more precise.

The other thing is, frankly, and I'm almost embarrassed to admit it now, I was so thrilled by the connection you speak of btw differentiable infinite tangents and "integrable" infinitely small rectangles, that I just had to express this joy in some form or another.... here seems like an obvious (and in my case, the unique) place to do it.

Yes, I have been reading up on Reinmann sums and yes, you are getting to know me: I love the theoretical, formal side, the deep, philosophically rich component to maths, the deep interconnections and surprising results that seem to be "mothered" by still deeper, more general theorems.

And so I intend to continue such reading and I actually see a future where I might read the history and philosophy of mathematics in some formal setting, but that's for later! right now, under my nose, is a lot of work to do, enjoyable and engaging work, but work nonetheless.

But you are so spot on to point out that such reading helps the practice of maths!!
And I'm sure a lot of educators have yielded to a counsel of despair in thinking that they cannot justify "burdening" their students with any more "baggage" than is absolutely necessary for them to "get through" their calculus course... the same desperate -inherently self-defeating - practice increasingly adopted by educators across the board, across the globe these days, I'm afraid.

Once again, thanks for your response and encouragement!

Deus Abscondus
(I wonder if he'll be back; I'm not holding my breath while I wait)

#### Jameson

Staff member
Moving beyond memorizing formulas on faith and starting to prove them or follow a proof is a great feeling. Whenever I tutor math at any level I almost never suggest memorizing something, instead reinforce concepts that apply to many formulas and situations. Most of the time it doesn't work that well - either the student wants a list of "tricks" or the approach needs more time to sink in. I've seriously read through solution manuals for a university entrance exam that say something like "Using tactic D-15 from this book the solution is ________". Anyway, I digress.

The last bit of your integral calculation 2 and 2/3 u-squared. Two things:

1) Where did the u^2 come from?
2) Why did you convert the fraction to a mixed number? Leaving it as an "improper fraction" is perfectly fine and the standard way to write a fraction unless told otherwise. Maybe you wrote it that way to show the area was between 2 and 3 square units.

I tried writing a mixed number in Latex just now but the spacing wasn't right.

EDIT: Just realized that u-squared is "units squared". Makes sense now. I also thought it strange to put units that weren't defined but understanding what units is so important that it's not a bad habit, and I know many teachers require this or the solution is considered incorrect.

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#### Fantini

MHB Math Helper
Jameson,
1. I thought that because what I have integrated is essentially an area that it should be written as squared units (since the unit of measurement isn't otherwise stipulated)
I may not be the best person to comment on this, but I believe we write "area units" or "a.u." in short. Squared units doesn't sound such a bad idea, though.