Could I use a LM324 quad op amp instead? The only dual op amp that my local radio shack seemed to have was a TL082 Dual Bifet Op Amp.It is very confusing for you to use a lousy old 741 opamp that needs a lot of changes to a simple circuit to make it work. The output of the 741 opamp does not go to a low enough voltage to turn off a red LED.
If you use an inexpensive and readily available LM358 or MC33172 dual opamp then they make an oscillator and an integrator that need only a single supply voltage. A transistor will not be needed.
Also, the more I read, the more it seems that the 555 is a big part of the problem since its output never really goes to zero.
Thanks again for all the help and patience. It's been frustrating trying to get this whole thing to work when it seems like it should be working.