Integrals

Hi /sci/

I'm having orals for a french computer engineering school (i'm french). Amongst those orals, there is a maths oral. The thing is, we didn't study integrals in class yet. And the book is f*** stupid. So could anybody clearly explain to me what integrals are, how they work, etc.

Thanks a lot ;)

Welcome to math and /sci/

Also, do your own homework

It's not homework. I'm getting ahead of the program, and I need a little help for that. That's all.

>> 3
Get a girlfriend.

Integrals are basically just antiderivatives. The Power Rule is the inverse...etc. The integral's applications, however, are far more useful.

>>5
 that depends on what science you're working with, but yes, the immdiate applicability of integrals is very cool.

anyways, as >>5 said, it's basically antiderivatives, that being, you find out "what would i have to derive in order to reach the wanted result".
So the integral of f'(x) is f(x).
now the geometrical interpretation would be that if you solve an integral defined over (a,b), you get the area underneith the graph from a to b.  Now, there is alot more to it than just that, but i can't remember it just now and i'd need to get my book etc. but i suggest you just wiki it, or buy your next math book in advance.

I am looking for the antiderivative to
f(x)=exp(-sqrt(x^2+a))
Does anyone know about a good resource to get this? My ass old version of derive fails at this.

>>7
unfortunately there is no analytic expression for that indefinite integral.

>>8
Damn, and it looked so harmless at first. No way to even solve it partly, through substituion or otherwise? Numerically solved it looks like it could be an arctan of sorts. Gonna seek the wisdom of Bronstein tommorow, maybe he will help.

>>9
actually i was thinking of a different integral. didn't read your question properly hehe. it might have a nice solution. but i can't help you cos i havent done integratio for almost 2 years.

>>7
i've been fiddling with this for half an hour and i know nothing, please confer to us the, hopefully, attained wisdom of Bronstein.

http://integrals.wolfram.com/

integrals are (basically) the reversal of differentiation.
d/dx(2x)=2
integral(2x)=x^2 + k
where k is some unknown constant
Obviously, they become rather more complex, and may have multiple different solutions.
Does that help any?
also:
http://fr.wikipedia.org/wiki/Int%C3%A9grale

>>7
That's a Gaussian...  I do not believe an analytic solutions exists as of 2007

The definite integral from -inf to inf exists though.

>>7
I'm only in calc 2, but in our text it says there is no elementary anti-derivative to that, but you can express it using power series or some voodoo magic?

>>13

Thanks a lot.

French engineers can't integrate?
Im not surprised.

>>15
yep and I like the trickery used to get it. (http://en.wikipedia.org/wiki/Gaussian_integral)

Just practice and get Mathematica.  Knowing how to use integrals is integral.