emma boulton
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- May 14, 2020
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hi
does anyone know how I would solve this question im really stuck.
does anyone know how I would solve this question im really stuck.
Laplace transform - split
- Thread starter emma boulton
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D
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Please show us what you have tried and exactly where you are stuck.
Please follow the rules of posting in this forum, as enunciated at:
https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520
Please share your work/thoughts about this assignment.
emma boulton
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- May 14, 2020
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This is my answer for part a) I can seem to work out how to get to the final answer for e^at and also i am confused about how you would get the ranges for these answers.
Sorry if my work is a bit messy its taken a while to get to this point
Sorry if my work is a bit messy its taken a while to get to this point
HallsofIvy
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- Jan 27, 2012
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You state in your first post that the Laplace transform of a function, f(x), is \(\displaystyle \int_0^\infty f(t)e^{-st}dt\). So why does the work you show not have any integrals?
The Laplace transform of \(\displaystyle f(x)= e^{-ax}\) is \(\displaystyle \int_0^\infty e^{-at}e^{-st}dt= \int_0^\infty e^{-(a+ s)t}dt\). Can you integrate that?
The Laplace transform of \(\displaystyle f(x)= Ax+ B\) is \(\displaystyle \int_0^\infty (Ax+ B)e^{-st}dt\). Integrate that using "integration by parts" with u= Ax+ B and \(\displaystyle dv= e^{-st}dt\).
The Laplace transform of \(\displaystyle f(x)= e^{-ax}\) is \(\displaystyle \int_0^\infty e^{-at}e^{-st}dt= \int_0^\infty e^{-(a+ s)t}dt\). Can you integrate that?
The Laplace transform of \(\displaystyle f(x)= Ax+ B\) is \(\displaystyle \int_0^\infty (Ax+ B)e^{-st}dt\). Integrate that using "integration by parts" with u= Ax+ B and \(\displaystyle dv= e^{-st}dt\).