| eat cos(bt) dt = eat a cos(bt) + b sin(bt) + C. a2 + 62 a. Use this antiderivative to compute the following improper integral: lim TH00 e4t cos (3t) e st dt = if s + 4 or -st dt et cos(3t) e Jo lim sin(3T)/3 T00 if s = 4. he (formulas)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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I am having trouble finding a solution to the equation in part a and part c.

eat
cos(bt) dt =
a cos(bt) + b sin(bt)
+ C.
eat
a2 + 62
a. Use this antiderivative to compute the following improper integral:
e4t
cos(3t) e
dt =
lim
T00
if s + 4
or
4t
e" cos(3t) e-st dt =
lim sin(3T)/3
T00
if s = 4. help
(formulas)
b. For which values of s do the limits above exist? In other words, what is the domain of the Laplace transform of et cos(3t)?
s>4
help (inequalities)
c. Evaluate the existing limit to compute the Laplace transform of et cos(3t) on the domain you determined in the previous part:
F(s) = L {e# cos(3t)} =
help (formulas)
Transcribed Image Text:eat cos(bt) dt = a cos(bt) + b sin(bt) + C. eat a2 + 62 a. Use this antiderivative to compute the following improper integral: e4t cos(3t) e dt = lim T00 if s + 4 or 4t e" cos(3t) e-st dt = lim sin(3T)/3 T00 if s = 4. help (formulas) b. For which values of s do the limits above exist? In other words, what is the domain of the Laplace transform of et cos(3t)? s>4 help (inequalities) c. Evaluate the existing limit to compute the Laplace transform of et cos(3t) on the domain you determined in the previous part: F(s) = L {e# cos(3t)} = help (formulas)
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