Hatrack River Forum: Math Question

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Posted by HollowEarth (Member # 2586) on :

Whats the integral of 1/dx? or (x^2)/dx?

My calculus skills seem to have left me.

Posted by Dagonee (Member # 5818) on :

*runs screaming from the building*

Posted by Shan (Member # 4550) on :

Do your own homework!

(snigger)

Posted by King of Men (Member # 6684) on :

Well, if I am understanding the question, you are trying to integrate with respect to the inverse of dx? I'm not totally convinced that is well defined, but it's been a long day and I haven't had dinner yet. Try using the chain rule to express (1/dx) in terms of just plain dx and some power of x. I'll have another look after dinner, when my brain is operating properly.

Posted by Stray (Member # 4056) on :

Argh, I should know these. Calculus wasn't that long ago [Wall Bash]

Posted by LockeTreaty (Member # 5627) on :

If I understand it correctly you are just asking for the integral of 1 and x^2. Those integrals would be x + C and (1/3)x^3 + C.

Posted by Bokonon (Member # 480) on :

That looks like it's a Differential Equations problem. I'd check my old textbook, but I'm not at home.

Argh!

-Bok

[ November 11, 2004, 05:51 PM: Message edited by: Bokonon ]

Posted by ssywak (Member # 807) on :

⌠dx = X + C
⌡

⌠x^2dx = (X^3)/3 + C
⌡

But 1/dx ??? That seems to point towards differentiation, not integration.

(Darn! Locke Treaty beat me to it!)

Posted by HollowEarth (Member # 2586) on :

Its a text book typo. I looked the formula up elsewhere. thanks though.

Posted by King of Men (Member # 6684) on :

Right. Blood sugar, amazing stuff. We have

d(1/x) = -(1/x^2)dx,

which should give you what you need.

Posted by ssywak (Member # 807) on :

That would be...

⌠(1/x^2)dx = -1/X + C
⌡

But...

⌠(1/x)dx = ln(X) + C
⌡

This is your homework, isn't it?

Posted by Bokonon (Member # 480) on :

So what was the question supposed to be? For the record, I coulda come up with the other solutions, but I was assuming the question was correct. So there. [Smile]

-Bok

Posted by HollowEarth (Member # 2586) on :

Well, it wasn't really homework. That is to say doing that integral was not a necessary part of my homework. It comes from a typo in

d[ΔGfus/T] = - (ΔHfus*dT)/T^2

Which through subsequent steps becomes an expression that relates the mole fraction to depressed freezing point in an ideal binary solid-liquid equilibrium system. This expression has various assumptions in it, for example that the ΔHfus is a constant between ~10 and ~90C, but it gives rather good results for a naphthalene/biphenyl system, ( < 1% error in experimental melting points)

I was attempting to work through the derivation myself, but hit this integral that i couldn't integrate, which it turns out, I didn't have to.

[ November 11, 2004, 07:04 PM: Message edited by: HollowEarth ]