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(1 point) a. Set up an integral for finding the Laplace transform of the following function: f(t) = { 0, 0 ? t < 4; t + 7, 4 ? t. F(s) = L {f(t)} = ?_A^B (t+7)e^(-st)dt where A = 4 and B = infinity . b. Find the antiderivative (with constant term 0) corresponding to the previous part. (-11e^(-4s)s+7s+1-e^(-4s))/(s^2) c. Evaluate appropriate limits to compute the Laplace transform of f(t): F(s) = L {f(t)} = (((1/s)+(1/(s^2)))e^(4s)) d. Where does the Laplace transform you found exist? In other words, what is the domain of F(s)? s>0

          (1 point)
a. Set up an integral for finding the Laplace transform of the following function:
f(t) = { 0, 0 ? t < 4; t + 7, 4 ? t.
F(s) = L {f(t)} = ?_A^B (t+7)e^(-st)dt
where A = 4 and B = infinity .
b. Find the antiderivative (with constant term 0) corresponding to the previous part.
(-11e^(-4s)s+7s+1-e^(-4s))/(s^2)
c. Evaluate appropriate limits to compute the Laplace transform of f(t):
F(s) = L {f(t)} = (((1/s)+(1/(s^2)))e^(4s))
d. Where does the Laplace transform you found exist? In other words, what is the domain of F(s)?
s>0

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(1 point)
a. Set up an integral for finding the Laplace transform of the following function:
f(t) = 0, 0 ? t < 4; t + 7, 4 ? t.
F(s) = L f(t) = ?A^B (t+7)e^(-st)dt
where A = 4 and B = infinity .
b. Find the antiderivative (with constant term 0) corresponding to the previous part.
(-11e^(-4s)s+7s+1-e^(-4s))/(s^2)
c. Evaluate appropriate limits to compute the Laplace transform of f(t):
F(s) = L f(t) = (((1/s)+(1/(s^2)))e^(4s))
d. Where does the Laplace transform you found exist? In other words, what is the domain of F(s)?
s>0

Added by Manuela F.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

09/09/2023

Step 1

Since the function is defined piecewise, we only need to consider the interval where the function is non-zero, which is 0 < t < 4. So, we have: $$F(s) = L\{f(t)\} = \int_0^4 (t+7)e^{-st} dt$$ Now, we need to find the antiderivative of the integrand. We can use Show more…

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a. Set up an integral for finding the Laplace transform of the following function: f(t) = { 0, 0 <= t < 4; t + 7, 4 <= t F(s) = L {f(t)} = integral from A to B (t+7)e^(-st)dt where A = 4 and B = infinity b. Find the antiderivative (with constant term 0) corresponding to the previous part. (-11e^(-4s)s+7s+1-e^(-4s))/(s^2) c. Evaluate appropriate limits to compute the Laplace transform of f(t): F(s) = L {f(t)} = (((1/s)+(1/(s^2)))e^(4s)) d. Where does the Laplace transform you found exist? In other words, what is the domain of F(s)? s>0

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