/sci/ - Science & Math

also, wouldn't dy/y equal just d?

Substitute
(x^2 + 2) dx = 1/3 dy
and
(x^2 + 6x -1 ) = y
into the equation on the left side.

>>6998684
No, dy is not d * y, it's a y-increments of infinitesimal length. Used in Leibniz notation derivatives.

d( x^2) / dx = 2x

>>6998688
What he said. Just take the derivative of y=x^3+6x-1 and divide both sides by 3 and multiply both sides by dx. Then you can plug in (x^3+6x-1)=y on bottom and (x^2+2)dx=(1/3)dy on top. Done. Also, the multiplication trick won't work for multivariable integrals. Then you'll need to play with Jacobians, but you're way too far off to worry about that yet.

>>6998688
>(x^2 + 6x -1 ) = y
>into the equation on the left side
I don't follow anymore.

My brain is full of fuck right now.

First of all, where the fuck does "y=" comes from? And why is it that only the denominator equals to y? Besides, we're talking about an empty integral here, there are no y values here! I mean, usually it looks like integral from 0 to 3 and some value is being integrated...
http://i.stack.imgur.com/bRXmz.jpg
for instance here, y values are from pi to 0

>>6998693
>Then you can plug in (x^3+6x-1)=y on bottom
woah, wait wait, hold on there a sec, how come


>Just take the derivative of y=x^3+6x-1
3x^2 + 6
>and divide both sides by 3 and multiply both sides by dx
but why are there both sides now? and how do you know left side must be "dy"?????
in any case, dividing both sides by 3 should give:
1/3 dy = (x^2 + 2)
then multiplying by dx
1/3 dy dx = dx (x^2 + 2)
I fail to see how as a next step I'd
>plug in (x^3+6x-1)=y on bottom
doesn't make sense...

pls respond

respond please

pls respond

d(ln(y(x))/dx = d(y(x)) / y(x)

work backwards from there

>>6998727
>ln
uhm, what? can you just answer something from this post >>6998709

>>6998728
Hmm, I think you should try learning about logarithms and indefinite integrals before worrying about this problem m8. It'll seem easy then.

>>6998709
>I don't follow anymore.
See image (sorry for amateur style formatting; need to reinstall LaTeX)

>where the fuck does "y=" comes from?
Plucked out of the sky. Once you learn the patterns you will generally be able to tell what kind of "y=...." to use. It's usually somewhere in the original formula.

>Besides, we're talking about an empty integral here, there are no y values here! I mean, usually it looks like integral from 0 to 3 and some value is being integrated...
You haven't done Indefinite Integrals yet? It's the same as normal integrals but instead of plugging the values in, you just plug in the variable you're integrating over (y here) and add C (an arbitrary constant since it disappears in the derivative).

>>6998770
image

>>6998691
>it's a y-increments of infinitesimal length
>not the exterior derivative of the 0-form y

Come on, man.

>>6998681
First y is chosen to be the denominator, so the integrand could be written as (x^2+2)/y dx. Then using the chosen y find dy/dx=eqn and substitute dy/eqn=dx into the integrand so it is now an integral over y instead. The problem has been designed so that "eqn" is equal to 3* the numerator and all of the xs cancel.

>>6998975
>I just looked up exterior algebra on Wikipedia so I can show off muh superior math knowledge in a chinese cartoon imageboard