For the first one, show that <cos(mx), sin(nx)> = 0. Also show that <cos(mx), cos(mx)> = 1 and that <sin(nx), sin(nx)> = 1.Last two inner product questions.
The first one I am little confused on and the second one I don't know what to do.
See worked attached.
Can you elaborate on this a bit more? You haven't said quite enough so that I'm not sure I understand what you're talking about. If you have a given integral on one side, and 1/(s - 1) times the same integral on the other side, add -1/(s - 1) times the integral to both sides, and then combine the two integrals using the rules of plain old fractions. At that point you can solve for the integral algebraically.On the integration by parts comment, I have an unrelated issue. I was doing a Laplace Transform of e^(-st+t)*sin(t) but after doing integration by parts, I had a form of the original with a 1/(s-1) time the integral so I cant subtract across to the other side. What can I do there since if I keep going it will an endless cyclical cycle?