# how do you do this integral

• November 3rd 2009, 09:37 AM
richard7893
how do you do this integral
sin(wt)cos(nwt) dt
• November 3rd 2009, 09:44 AM
Jameson
Quote:

Originally Posted by richard7893
sin(wt)cos(nwt) dt

$u=\cos(nwt)$

Make this integral into the form of udu and it integrates easily.
• November 3rd 2009, 09:52 AM
richard7893
But if you do this your du=-nwsin(nwt). By doing this you cant substitute for sin(wt) because du=-nwsin(nwt)
• November 3rd 2009, 10:41 AM
Jameson
Quote:

Originally Posted by richard7893
But if you do this your du=-nwsin(nwt). By doing this you cant substitute for sin(wt) because du=-nwsin(nwt)

Ooops! Sorry I missed that. Eyes are wearing out from looking at the computer.

Hmmm, my first thought is to try the product to sum conversation for sin(a)cos(b), which looks like:

$\sin(a)\cos(b)=\frac{\sin(a+b)+\sin(a-b)}{2}$

That should split up into things you can integrate separately easily.