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[Darvi]

note to self: stick to science, keep math low-profile.

Now you're contradicting yourself.

Also I just noticed why I suck at integrating xP

[Tellemurius]

what? i rather work on my geology and chemistry, im never bringing a question here.

[Leafsnail]

Also I just noticed why I suck at integrating xP

You're integrating xP with respect to what?

[Darvi]

Also I just noticed why I suck at integrating xP

You're integrating xP with respect to what?

Nice one

It's just when integrating u(x)*v'(x), I always turn that into

u(x)v(x)-integral(u'(x)v(x))dx

instead of

integral(u(x)v(x))dx-integral(u'(x)v(x))dx

[Christes]

Actually, the first one is correct.  You shouldn't integrate u(x)v(x).  Try a simple counterexample where u(x)=1 and v(x)=1.

You just need to make sure you plug the endpoints in there when you are taking a definite integral.  I remember it as just being the product rule (for differentiation), but in reverse.

[Darvi]

Bluh router's being an arse again, so double post.

[Darvi]

Yeah I got that mixed up again >_> I actually meant it the other way round.

[Leafsnail]

Funnily enough, that's exactly what I'm set to do in my next calculus lesson :p.

[Nivim]

 I'm glad you figured out your problem Vector; willing to fill it in and cap it off for those obfuscated by it?

[Vector]

I'm glad you figured out your problem Vector; willing to fill it in and cap it off for those obfuscated by it?

Sure.  Did you understand what I said about the volumes of inscribed prisms approaching the volume of the cylinder as the number of sides increases?

[Nivim]

 Yes, as long as the vertices of the prism stay on the surface of the cylinder it would take an infinite number of vertices for the prisms volume to match that of a cylinder...but I thought limits were calculus.

[Christes]

Not in the modern sense, but the Greeks could take limits in a de facto geometric sense.

The history of limits is rather complicated and full of shades of grey.

[Vector]

Yeah, exactly.  So then you do that on the outside and the inside, and trap the volume of the cylinder between the two approximations.

[Darvi]

That's pretty much how the Greek got a good approximation to Pi, but in the third dimension.

I think it was Archimedes or something.

[Christes]

Yeah, exactly.  So then you do that on the outside and the inside, and trap the volume of the cylinder between the two approximations.

So it's basically the same way you calculate the area of the circle - it's just that the hard work is already done for you?  I like proofs like that.