Question

1. Find the Laplace transforms of the following functions. a. f(t) = (t + 2)^2 e^t b. f(t) = e^{-4t} cosh 2t c. f(t) = t^3 e^{-3t} d. f(t) = t cos t e. f(t) = 1/sqrt(t) Hint: Make a change of variable x = sqrt(st). f. f(t) = sin t / t g. f(t) = integral_0^t sin tau d tau

          1. Find the Laplace transforms of the following functions.
a. f(t) = (t + 2)^2 e^t
b. f(t) = e^{-4t} cosh 2t
c. f(t) = t^3 e^{-3t}
d. f(t) = t cos t
e. f(t) = 1/sqrt(t) Hint: Make a change of variable x = sqrt(st).
f. f(t) = sin t / t
g. f(t) = integral_0^t sin tau d tau

1. Find the Laplace transforms of the following functions.
a. f(t) = (t + 2)^2 e^t
b. f(t) = e^-4t cosh 2t
c. f(t) = t^3 e^-3t
d. f(t) = t cos t
e. f(t) = 1/sqrt(t) Hint: Make a change of variable x = sqrt(st).
f. f(t) = sin t / t
g. f(t) = integral0^t sin tau d tau

Added by Oscar V.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

09/13/2023

Step 1

For f(t) = (t + 2)^2 * e^t, we have: $$\mathcal{L}\{ (t + 2)^2 e^t \} = \int_0^\infty (t + 2)^2 e^{-(s - 1)t} dt$$ Using integration by parts twice, we get: $$\boxed{\mathcal{L}\{ (t + 2)^2 e^t \} = \frac{2 + 4(s - 1) + (s - 1)^2}{(s - 1)^3}}$$ Show more…

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Find the Laplace transforms of the following functions: a. f(t) = (t + 2)^2 e^t b. f(t) = e^(-4t) cosh 2t c. f(t) = t^3 e^(-3t) d. f(t) = t cos t e. f(t) = 1/sqrt(t) Hint: Make a change of variable x = sqrt(st) f. f(t) = sin t / t g. f(t) = integral_0^t sin tau d tau