Laplace Convolution proof - can someone please explain the diagram

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The discussion centers on the Laplace Convolution proof, specifically addressing the understanding of a diagram related to the area of region R and its connection to signals f and g. The user, Thomas, derived the proof by altering the time limit to infinity and seeks clarification on the significance of the diagram in relation to the convolution theorem. The reference provided by Thomas offers additional context but does not fully resolve the user's confusion regarding the diagram's implications.

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thomas49th
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Homework Statement


http://gyazo.com/22f5c655071e49adf3f4652e8042873b


I derived the proof myself, but by arbitrary changing the t limit to infinity. I'm hoping that by understanding the diagram in the link above I will have a better idea of why I changed the limit. I currently look at it as we are finding the area of region R, but what does that have to do with signals f and g?

Thanks
Thomas
 
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also found a reference here

http://math.fullerton.edu/mathews/c2003/laplacetransform/LaplaceConvolutionTheorem.1.pdf

Still not really getting the point of the diagram
 
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