Calculus

[peterhuang913]

but if you substitute tan(x)^2 with dv, it doesn't get rid of the dx.

 

[Merkwürdigeliebe]

what's the derivative of x?

ie what is dx?

 

[peterhuang913]

I still don't know why you can isolate and take out that part.

The next step is / u dv right? How do you get to the next step.

 

[Merkwürdigeliebe]

it's just convention to have dx at the end of an integral expression, it's completely unnecessary though, because dx (derivative of x) is 1, so you're multiplying the expression by 1 which doesn't do anything of course

du and dv (and so on) are neccesary in substitution because they usually represent more important expressions that will change the result as a whole, like du in the original problem; derivative of u (= tan²x) is [tanx-x]

and '/ u dv' came from here:

 

[peterhuang913]

ok i get that part.

next, how does / u dv become dv - / v du

 

[Merkwürdigeliebe]

ok i get that part.

next, how does / u dv become dv - / v du

that's just a formula that's expected to be memorized, the proof is rather long and complicated

here it is:

 

[peterhuang913]

can you please show me? also, thank you very much for taking your time to explain this to me.

 

[Merkwürdigeliebe]

can you please show me? also, thank you very much for taking your time to explain this to me.

yeah I just attached the proof in my last post, but tbqh, I don't even know how to explain the proof myself

I like explaining it because it helps me understand it better

(yeah that's wiki btw)

 

[peterhuang913]

Yea, I'm trying to learn too. Is that wiki?

 

[countrydude]

just wait till linear algebra! yaaay : ) Can't help you guys though I already forgot all that calculus stuff.