Question about calculus

[Dofuss3000]

When you solve for the equation

dy/dx = f(x)
dy = f(x)dx

by integrating it turns into y = (long s)f(x)dx

How does dy turn into y?

Any help would be great, thanks!

 

[2Xtreme21]

Because you took the anti-derivative of the derivative of y-- the inverse operation. Let me put it to you in another way:

y/2 = x + z

To solve for y, multiply (the inverse of dividing-- the form it is currently in) both sides of the equation by 2:

y = 2 * (x + z)

In your equation dy = f(x)dx, when you say "integrating it" you're integrating both sides of the equation.

 

[Heller]

Link to 'RickRolling' bomb removed, see you in two weeks.
Anandtech Moderator - bsobel

 

[NatePo717]

Originally posted by: Heller
This might help

I hate you.....

 

[2Xtreme21]

Originally posted by: Heller
This might help

BAN! Don't click on this link. -_-

 

[Heller]

wow...tough crowd

 

[PrinceofWands]

Originally posted by: Heller
wow...tough crowd

You know, after your other little link bs I've come to the conclusion you're nothing but a worthless little pr!ck desperately in need of a few weeks off.

 

[Heller]

Originally posted by: PrinceofWands

Originally posted by: Heller
wow...tough crowd

You know, after your other little link bs I've come to the conclusion you're nothing but a worthless little pr!ck desperately in need of a few weeks off.

Im just going to go ahead and say.

LoLuMad?

 

[silverpig]

Originally posted by: PrinceofWands

Originally posted by: Heller
wow...tough crowd

You know, after your other little link bs I've come to the conclusion you're nothing but a worthless little pr!ck desperately in need of a few weeks off.

He's been doing it in several threads now.

 

[PrinceofWands]

Originally posted by: Heller

Originally posted by: PrinceofWands

Originally posted by: Heller
wow...tough crowd

You know, after your other little link bs I've come to the conclusion you're nothing but a worthless little pr!ck desperately in need of a few weeks off.

Im just going to go ahead and say.

LoLuMad?

Not at the link, since I'm not stupid enough to click the things you post. I'm just mad that ignorant little twats like you don't get themselves punched in the face enough to learn some basic decency. Hopefully someone will correct that oversight in your life sometime soon.

 

[silverpig]

Originally posted by: Dofuss3000
When you solve for the equation

dy/dx = f(x)
dy = f(x)dx

by integrating it turns into y = (long s)f(x)dx

How does dy turn into y?

Any help would be great, thanks!

The integral of dy is y. You kind of skipped small step:

dy = f(x)dx

Integrate both sides
Int[dy] = Int[f(x)dx]

On the left we have:
Int[dy] = y

And on the right we are still doing generally, thus
y = Int[f(x)dx]


Going back to Int[dy] = y we can use the fundamental theorem of calculus to differentiate both sides:

d(Int[dy]) = d(y)

the 'd' undoes the Int[] leaving

dy = dy which is the expected result.

 

[George P Burdell]

Originally posted by: Dofuss3000
When you solve for the equation

dy/dx = f(x)
dy = f(x)dx

by integrating it turns into y = (long s)f(x)dx

How does dy turn into y?

Any help would be great, thanks!

The easiest way to understand this is to go back to when you were first introduced to calculus and the concept of area under a curve. While the best place to read this up is ye olde Calculus book, you can start with Wikipedia

http://en.wikipedia.org/wiki/Integral#Introduction

 

[Tiamat]

Originally posted by: 2Xtreme21

Originally posted by: Heller
This might help

BAN! Don't click on this link. -_-

DAMN IT! I didnt read your warning

BAN HIM!!!

 

[BrownTown]

Originally posted by: 2Xtreme21

Originally posted by: Heller
This might help

BAN! Don't click on this link. -_-

SECOND the bannage motion.

 

[Taejin]

Originally posted by: Heller
This might help

can a mod please ban this guy? I guess he thinks his links are funny, but they're just incredibly annoying.

if you're using firefox and you want to close his window just disable javascript under tools/options first

 

[zerocool1]

Originally posted by: Tiamat

Originally posted by: 2Xtreme21

Originally posted by: Heller
This might help

BAN! Don't click on this link. -_-

DAMN IT! I didnt read your warning

BAN HIM!!!

neither did i