The signal x(t) = 2^(-t*u(t)) is defined as a piecewise function, where x(t) equals 1 for t < 0 and 2^(-t) for t > 0. The square of the signal, x(t)^2, also follows a piecewise definition: it is 1 for t < 0 and 2^(-2t) for t > 0. When integrating x(t)^2 from -1 to 1, the integral splits into two parts: from -1 to 0, the integral is 1, and from 0 to 1, it is the integral of 2^(-2t). The discussion focuses on verifying the correctness of the calculations and the approach taken for sketching the signal. The analysis emphasizes the importance of understanding piecewise functions in signal processing.
