how do you do this integral

richard7893 · #1 $Old$ November 3rd, 2009, 10:37 AM

sin(wt)cos(nwt) dt

Jameson · #2 $Old$ November 3rd, 2009, 10:44 AM

Quote:

Originally Posted by richard7893 $View Post$

sin(wt)cos(nwt) dt

$u=\cos(nwt)$

Make this integral into the form of udu and it integrates easily.

richard7893 · #3 $Old$ November 3rd, 2009, 10:52 AM

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

Jameson · #4 $Old$ November 3rd, 2009, 11:41 AM

Quote:

Originally Posted by richard7893 $View Post$

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.