b. Evaluate L{sin(at)}. f(t) = sin(at) F(s) = L{sin(at)} = e-st (sin(at))dt е 1 =-=-e-st sin(at) | | ² - 3 / ² - • a cos(at) 1 S $2 [-3/²6² e e-st (sin(at))dt

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.2: Trigonometric Equations
Problem 106E
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please explain how the last terms were obtained using integration by parts because I do not get how they were obtained. Please show clear solution on paper, do not just type the solution. 

b. Evaluate L{sin(at)}.
f(t) = sin(at)
F(s) = L{sin(at)} = *e-st(sin(at))dt
0
1
1
=-=e-st.sin(at)
S
-
1
a cos(at)
[-36²
fe
e-st (sin(at))dt
Transcribed Image Text:b. Evaluate L{sin(at)}. f(t) = sin(at) F(s) = L{sin(at)} = *e-st(sin(at))dt 0 1 1 =-=e-st.sin(at) S - 1 a cos(at) [-36² fe e-st (sin(at))dt
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