Need to find the integral of the following function using Laplace Transform int_0^(oo) (cos(6t)-cos(4t))/(t)dt

Gaige Haynes 2022-09-15 Answered
Need to find the integral of the following function using Laplace Transform
0 cos ( 6 t ) cos ( 4 t ) t d t
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Answers (1)

Baluttor7
Answered 2022-09-16 Author has 17 answers
Hint : write it as
0 cos 6 t cos 4 t t e s t d t
Where s= 0
Now it become Laplace transformation
L ( cos 6 t cos 4 t t )
We have property
L ( f ( t ) t ) = s F ( s ) d s
Here F ( s ) = L ( f ( t ) )
Using above property
L ( cos 6 t cos 4 t t ) = s ( s s 2 + 6 2 s s 2 + 4 2 ) d s
Integrate you will get
= 1 2 ln ( s 2 + 4 2 s 2 + 6 2 )
Now put s=0
=
= 1 2 ln ( 4 2 6 2 )
= ln ( 2 / 3 )

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