# Solving integration by parts using derivatives vs differentials?

1. Aug 20, 2011

### thepatient

What is the difference? I was pretty bored last night so I got onto Yahoo Answers and answered a few calculus questions. It was a simple integration by parts question:

$\int$xsin(x) dx

I solved as:
u = x
du = dx

dv = sin(x) dx
v = -cos(x)

uv - $\int$vdu
-xcos(x) + $\int$cos(x)dx = sin(x) - xcos(x) + c

I later got a thumbs down by a second answerer, saying that solving using differentials is much more difficult to do, and that it's preferable to answer using derivatives.

I don't understand. I mean, I know how to solve using derivatives and functions instead of differentials, but how is it more difficult, and how is it the wrong approach? It just kept bugging me all night since I have always solved in this form and never thought it was wrong or difficult. There is no big difference solving with functions either:

$\int$ f'(x)g(x) dx = f(x)g(x) - $\int$f(x)g'(x)dx

Only that you choose for a function and a derivative of a function. Am I missing something fundamental? Maybe I'm being too sensitive. I don't like getting thumbs down when I know I did something right. :( lol Any insight would be greatly appreciated. Thanks

2. Aug 20, 2011

I think the person who* thumbed you down wasn't sane lol

Last edited: Aug 20, 2011
3. Aug 20, 2011

### thepatient

I didn't thumb him down, he thumbed me down because I used a "more difficult approach". :( I believed him since he is a "top contributor", but I don't see how it's a more difficult approach. I just really feel I'm missing something.

I rarely thumb down. Only used it for things that don't answer a question, spam, trolls and very very very bad answers. XD

4. Aug 20, 2011

It was a typo xP
I believe both work well. And in mathematics it's useless to talk about preferred arguments I think. we got valid and invalid arguments. if your argument is valid, then who cares if there is an easier valid argument? both methods work fine and just because one method is few lines longer it doesn't make it an inferior or less preferred method.
I also like easy and beautiful proofs. but it doesn't mean that if you prove something in a way that someone doesn't prefer it he should thumb you down.

5. Aug 21, 2011

### thepatient

Ah... I messaged him and found out why he said such thing.. Apparently it is more difficult because you might forget the dx on the notation. And using functions and derivatives is more elegant, according to him. I didn't argue. I looked at my answer and did make a mistake on the notation and added an extra dx accidentally. Just a typo. XD