We use the known result for Laplace transform of a derivative sF(s) to speculate about the result for the transform of an integral. We guess that it might involve division by s. This result is proven using a double integration method.

Laplace transform of an integral using reversal of order of a double integral (MathsCasts)

These MathsCasts were produced by the mathematics support centres at Swinburne University, the University of Limerick and Loughborough University. They were part of a collaborative research project to develop high quality resources and investigate the effectiveness of MathsCasts to support mathematics learning. The full set of resources are available at http://commons.swin.edu.au/s/mathscasts MathsCasts are licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License

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Laplace transform of an integral using reversal of order of a double integral (MathsCasts)

Laplace transform of an integral using reversal of order of a double integral (MathsCasts)