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#1 2005-12-13 18:09:08

mikau
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Integration

Sometimes my book tells me to integrate on a graphing calculator, but I like to do it manually as well for practice. But once in a while I find something I can't seem to integrate.

integrate e^(-x^2)

If its original form had been e^(-x^2),  differentiating would have produced -2x e^(-x^2)   We can't go back to the original integral and say -1/2x * integral of -2x e^(-x^2) because you are not allowed to use variables when you do that. (don't ask me why)

Are some functions inpossible to integrate manually?

Keep in mind I'm about half way through my calculus book. They may teach me how to integrate a function like this in a later lesson. But perhaps I should already know how, and I'm forgeting something. Or perhaps some functions can not be integrated manually. Which is it?


A logarithm is just a misspelled algorithm.

#2 2005-12-13 19:12:10

Flowers4Carlos
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Re: Integration

i tried working out ∫e^(-x^2)dx but i wasn't able to go n e where w/ it.  i guess we need a super computer for this one.  *shrugs*

your half way through calculus??  wow... ur pretty fast.  are you learning it on your own or in an accelerated course???

#3 2005-12-13 23:22:19

mathsyperson
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Re: Integration

No, that one can't be integrated. At least, no one has discovered how to. But it also hasn't been proven to be impossible, so feel free to have a go and make yourself famous forever.

Until then, you can estimate the integral between two points by using numerical methods (Newton-Raphson, etc.) but you can't get the integral as an algebraic function.


Why did the vector cross the road?
It wanted to be normal.

#4 2005-12-14 10:06:14

mikau
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Re: Integration

I see. Thanks!

your half way through calculus??  wow... ur pretty fast.  are you learning it on your own or in an accelerated course???

I teach myself with a book. Saxon Calculus. All Saxon math books are great. Taught myself Algebra 1, 2 and Trig with them, and now calculus. Its a pretty long book, longer then the other ones, and calculus seems to take longer then I anticipated. Before I did 3 lessons a day and would tear through a book in about two months. (interuptions included) but calculus I usually only end up finishing one or two lessons a day. But sometimes you start to speed up as you get more familiar with the concepts, and learning and doing the problems gets easier.


A logarithm is just a misspelled algorithm.

#5 2005-12-14 13:56:58

irspow
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Re: Integration

I too taught myself algebra, trig, and calculus, and I commend you for doing so.  I dropped out of school in eighth grade, but went to college for engineering some 15 years later.  The university wouldn't even let me matriculate until I had earned 20 credits because they thought that I had no shot.  Actually I tested out of 3 of my calculus classes without ever stepping foot in a classroom.  I asked the head of the math department if I could simply go over the texts on my own and be tested by him directly when I felt comfortable with the material.  Thankfully he agreed to allow me to do so.
   It was hard at times, especially with calculus.  Some concepts are grasped right away and others must be gone over and over until it finally sinks in.  If you had the motivation to do this much on your own, you will be just fine.  Some people just enjoy learning.  Good luck on your continuing studies.
   P.S.  When you become proficient in differential equations maybe you could help me out!

#6 2005-12-14 16:21:05

Ricky
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Re: Integration

It's not quite impossible.  Well, that also depends on your definition of impossible.

You can represent e^-(x^2) as an infinite series, in which case you can intergrate it.  You'll still be left with an infinite series, but you can do it...

On the other hand, if you're looking for a simple function (i.e. non-infinite series), then it is impossible, at least to current knowledge.

Last edited by Ricky (2005-12-14 16:22:56)


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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