What is e^{-at}sin(w)t*u(t) ?

The solution to e^{-at}sin(w)t*u(t) is e^{-at}t^2usin(w)

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simplify e^{-at}sin(w)t*u(t)

simplify

e^{- a t} sin (w) t \cdot u (t)

e^{- a t} t^{2} u sin (w)

Solution steps

e^{- a t} sin (w) t u (t)

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

tt = t^{1 + 1}

= e^{- a t} sin (w) u t^{1 + 1}

Add the numbers:

1 + 1 = 2

= e^{- a t} sin (w) u t^{2}

\frac{1}{3} π (5)^{2} (5)

33.4 \cdot π \cdot 1 0^{- 3}

- \frac{1}{6} r^{- 6} d r

\frac{3}{185}

e^{- 7.434}

What is e^{-at}sin(w)t*u(t) ?
The solution to e^{-at}sin(w)t*u(t) is e^{-at}t^2usin(w)