Specialist's Specialist Thread

[Special At Specialist]

So then I was correct in saying ∫dy = ∫2x dx ? I wouldn't lose any marks for that, would I?

[pi]

So then I was correct in saying ∫dy = ∫2x dx ? I wouldn't lose any marks for that, would I?

Nope

[Jenny_2108]

So then I was correct in saying ∫dy = ∫2x dx ? I wouldn't lose any marks for that, would I?

Nope

Do we have to write step by step like this in exam? :O
Its just tedious and time-consuming

[BubbleWrapMan]

Yeah you can probably omit that step in an exam. VCAA's not that pedantic about being mathematically correct.

[#1procrastinator]

Yeah, I've never seen that step done in any calculus text before

[Special At Specialist]

I don't think the step is necessary, but if I were to add it, then I wouldn't lose any marks for it.

[Jenny_2108]

I don't think the step is necessary, but if I were to add it, then I wouldn't lose any marks for it.

why do you have to add it if its not neccessary?
Btw, I dont see people solve by writing as  ∫dy = ∫2x dx though

[pi]

I liked writing as many steps as I could, just to avoid confusion by skipping steps.

His step mentioned ∫dy = ∫2x dx is a perfectly valid one and I've seen it written by few in my school.

[#1procrastinator]

Doesn't that
 mean you're then integrating dy? Shouldn't you be treating dy/dx as a function and not be treating it as a fraction?

[pi]

Doesn't that
 mean you're then integrating dy? Shouldn't you be treating dy/dx as a function and not be treating it as a fraction?

dy/dx obeys fraction laws. Perfectly legit.

[#1procrastinator]

hmmm...just seems a bit like abuse of notation to me lol

[pi]

hmmm...just seems a bit like abuse of notation to me lol

Technically it kind of is if you are a stickler to proper notation and nothing less than that, but it's pretty well accepted by VCAA and by most mathematicians in general.

[Hutchoo]

hmmm...just seems a bit like abuse of notation to me lol

dy/dx is treated as a normal fraction. That's how the chain rule works.

Note: d^2y/dx^2  (or any type of differential that's higher than the first derivative cannot be treated as a fraction).

[BubbleWrapMan]

I wrote on the last page:

That's where the ∫dy comes from, so it's a valid step to write ∫dy = ∫f(x)dx after dy/dx = f(x), it just skips the derivation of it in the first line (above). So I guess if you write the second line you might as well write the first line. But yes, ∫dy is valid.

[rife168]

hmmm...just seems a bit like abuse of notation to me lol

You're right:
http://en.wikipedia.org/wiki/Abuse_of_notation#Derivative