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 June 17th, 2019, 01:49 PM #1 Senior Member   Joined: Oct 2015 From: Greece Posts: 137 Thanks: 8 How to solve this simple Laplace integral? Check this Image. I tried to post it as an image but it takes the entire space of the post... It seems I have forgotten a lot about solving integrals... But I really need to remember quickly how to solve this kind of fractional integrals since I haven't memorized the Laplace "trick" formulas (like 1 over Laplace is $\displaystyle \frac{1}{s}$) and tomorrow I have a test. Last edited by babaliaris; June 17th, 2019 at 01:53 PM. June 18th, 2019, 01:18 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,978 Thanks: 2229 I can't see the image for some reason. Can you just type enough to explain what the integral is? June 18th, 2019, 03:55 AM   #3
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Attached Images vsfiPnN.jpg (94.4 KB, 7 views) June 18th, 2019, 05:37 AM #4 Senior Member   Joined: Oct 2015 From: Greece Posts: 137 Thanks: 8 By the way I finished the test today, and it was 90% of Fourier transformation exercises while in the past you had like one exercise only... I probably failed the test and the weird thing is that i knew how to solve the integrals... The problem is that the textbook says that $\displaystyle \mathcal{L} = \frac{1}{s}$ but if I try to calculate it, $\displaystyle \mathcal{L} = \lim_{T->\infty} \int_{-T}^{T} 1 \cdot e^{-st} dt = \lim_{T->\infty} [\frac{e^{-st}}{-s}]_{-T}^{T} = \lim_{T->\infty} [\frac{e^{-sT}}{-s} - \frac{e^{sT}}{-s}] = \frac{1}{s} \lim_{T->\infty} [-e^{-sT} + e^{sT}]$ I believe that $\displaystyle \lim_{T->\infty} [-e^{-sT}] = 0$ and $\displaystyle \lim_{T->\infty} [e^{sT}] = \infty$ by trying to "see it" using the graph below. But of course this is not true, because the limit of them both must be 1 in order to get $\displaystyle \frac{1}{s}$ This is a really great problem that is keeping me from calculating Laplace integrals in general. I certainly need to review calculus all over again, but I have no time... I will try this summer though.... This limit is extremely easy and yet I don't remember how to solve it. Offtopic: How did you put that image into a thumbnail? When I try to add a big image in a post usually it takes over the whole screen. Last edited by babaliaris; June 18th, 2019 at 05:43 AM. June 18th, 2019, 11:14 AM   #5
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 Originally Posted by babaliaris How did you put that image into a thumbnail?
Post as an attachment instead of a URL. Tags integral, laplace, simple, solve Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post babaliaris Algebra 1 June 11th, 2018 09:06 AM doctordino Differential Equations 1 February 1st, 2016 11:45 AM jiasyuen Calculus 1 April 20th, 2015 12:36 PM shreddinglicks Differential Equations 1 December 7th, 2014 01:27 AM szz Calculus 3 October 26th, 2014 02:17 PM

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