Understanding Integration by Substitution

[Delzac]

Homework Statement

[PLAIN]http://img293.imageshack.us/img293/5026/solutoni.png

Hi all,

Can anyone explain what is going on where? I understand that it is a different way of writing the conventional integration by substitution, instead of using the symbol u. The second line, however, especially confuse me. I don't understand how the working changes between d(sin2010x) and dx.

The Attempt at a Solution

I used integration by parts and worked out the answer to be zero.

Double checked with online integration calculator.

Any help would be greatly appreciated.

Delzac

 

[tiny-tim]

Hi Delzac!

The second line, however, especially confuse me. I don't understand how the working changes between d(sin2010x) and dx.

As you say, it start by avoiding using a "u".

The jump you don't understand is an integration by parts in which the […] bit has been omitted because it's zero.

(never do that in an exam!)

The whole thing is just a (to my mind) rather long-winded and confusing way of doing two successive integrations by parts.

 

[Delzac]

Oh! now i see. Thanks for the help!

Delzac