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**Skruven** Determine i(t)

$\displaystyle {i}'(t) + 4i(t) + 5\int_{0}^{t}i(\tau )d\tau = \delta (t-2)$

$\displaystyle t>0, i(0)=0$ where $\displaystyle \delta (t-2)$ is a dirac delta function

i(t) is the current, with laplace transformation i got $\displaystyle i(t) = \frac{1}{2}e^{((-2-i)(t-2)))}((1+2i)e^{(2i(t-2))}+(1-2i))\theta (t-2)$

where $\displaystyle \theta (t-2)$ is a heaviside function

then they ask of $\displaystyle \lim_{t \to \infty }\int_{0}^{t}i(\tau )d\tau$ i think it will be 0 but how do i see that? do i really need to integrate my i(t)?

regards!