From a table of integrals, we know that for a, b ne 0, integral e^at cos(bt) dt

Question

From a table of integrals, we know that for a, b ne 0, integral e^at cos(bt) dt = e^at. a cos(bt) + bsin(bt)/a^2+b^2 + C. Assume W is a constant, and use this antiderivative to compute the following improper integral: integral_0^infinity cos(wt) e^-st dt = lim_T rightarrow infinity if s ne 0 integral_0^infinity cos(wt) e^-st dt = lim_T rightarrow infinity if s = 0. For which values of S do the limits above exist? In other words, what is the domain of the Laplace transform of cos(wt)? Evaluate the existing limit to compute the Laplace transform of cos (wt) on the domain you determined in the previous part: F(s) = L{cos(wt)} =

Explanation / Answer

1) L(coswt)

(apply the formula for laplace transform)

2)The limit of s is 0 to infinity.

that means s>0

3)L(cos(wt)) = s/(s2+w2), where s>0

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