Question: The impulse response of an LTI continuous-time system is such that h(t) = 0 for t ≤ T1 and for t ≥ T2 Show that if x(t) = 0 for t ≤ T3 and for t ≥ T4 then y(t) = x(t) * h(t) = 0 for t ≤ T5 and for t ≥ T6. In the process of proving this result you should obtain expressions for T5 and T6 in terms of T1 , T2, T3, and T4. The best way to work this problem is to draw "flip and slide" pictures for typical input and impulse response signals (e.g., rectangular pulses).
Another way to approach this problem would be to use the condemn GUI to generate some examples of convolving finite-duration signals, and then deduce the correct answer from those examples.