Laplace transform of $ \frac{1}{C}\int_0^1i(t)dt$

Question

I have the integral:

$$ \frac{1}{C}\int_0^1i(t)dt$$ which I should transform with Laplace. There is a rule saying that $$ \int_0^ti(t)dt$$ has the transform $$ s^{-1}F(s) $$ can I use this to transform my integral? The only difference is that t is 1, and I dont really know how that affect the rule stated above.

Answer 1

Note that the Laplace transform, transforms a function from the $t$-domain to the $s$-domain, now, notice that $\int\limits_0^1 {i(t)dt} $ is not a varying function of $t$, but a constant. Hence, its Laplace transform is equal to $\frac{1}{s}$ multiplied by itself (I suggest you use different notations for the dummy variable of the integral to avoid such ambiguities).