Use Laplace transform (with respect to t)to calculate the integral I=\int([\cos(tx)/(x^2+a^2)]dx t\geqslant 0 [IMG]file:///C:/Users/Jamie/AppData/Local/Temp/msohtmlclip1/01/clip_image002.jpg[/IMG]
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Originally Posted by sublim25 Use Laplace transform (with respect to t)to calculate the integral I=\int([\cos(tx)/(x^2+a^2)]dx t\geqslant 0 [IMG]file:///C:/Users/Jamie/AppData/Local/Temp/msohtmlclip1/01/clip_image002.jpg[/IMG] So you have but what are the limits of integration?
Limits are from 0 to infinity.
Let Then Now by partial factions we get Now if you take the inverse Laplace transform we get
Can you please explain how you get the partial fractions to come out to this?
Originally Posted by sublim25 Can you please explain how you get the partial fractions to come out to this? Now expand all of this out to get So this gives 4 equations in the 4 unknowns A,B,C,D dont forget that s and a are constants. Now just solve this system.
I am not sure what I am doing wrong, but when I solve the system, everything is cancelling out.
Originally Posted by sublim25 I am not sure what I am doing wrong, but when I solve the system, everything is cancelling out. I don't know either. Please post what you have done. Note that both A and C are equal to 0.
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