Sketching Signal x(t): 2^(-t*u(t))

[drkidd22]

Homework Statement

Sketch the signal:
x(t) = 2^(-t*u(t)) over (-1 < t < 1)

The Attempt at a Solution

Attached is an excel fine with my work out. I want to know is it is correct.

 

[xcvxcvvc]

It is simplest to think of this as a piecewise function
$$x(t) = \begin{cases}<br /> 1, t < 0 \\<br /> 2^{-t}, t>0<br /> \end{cases}$$
then
$$x(t)^2 = \begin{cases}<br /> 1, t < 0 \\<br /> 2^{-2t}, t>0<br /> \end{cases}$$
so when you integrate x(t)^2 from -1 to 1, it breaks apart into two integrals. One is from -1 to 0 of 1, and the other is from 0 to 1 of 2^{-2t}.