Calculate Energy of Signal x(t) = e(-2t) * u(t)

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The discussion focuses on calculating the energy of the signal x(t) = e^(-2t) * u(t). The energy is defined as Ex = ∫ x^2(t) dt, leading to the expression (e^(-2t))^2 = e^(-4t). Participants clarify the exponentiation of the exponential function and confirm the correct application of properties of exponents. The conversation highlights the confusion around squaring the exponential term and encourages further progress from that point. The key takeaway is the correct simplification of the squared term to facilitate the energy calculation.
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Homework Statement



x(t) = e(-2t) * u(t)

Ex = x2(t) dt

Attached is the work I have done. Got stuck towards the end.
 

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(e^{-2x})^2 = e^{-2x}e^{-2x}=e^{-2x-2x}=e^{-4x}
or you can use the power property associated with exponents and instantly say
(e^{-2x})^2=e^{2(-2x)}=e^{-4x}
I'm assuming the exponential being squared is what messed you up, and I'm assuming you can take it from here.
 

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