Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Ask your questions and receive accurate answers from professionals with extensive experience in various fields on our platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
With convolution theorem the equation is proved.
According to the statement
we have given that the equation and we have to evaluate with the convolution theorem.
Then for this purpose, we know that the
A convolution integral is an integral that expresses the amount of overlap of one function as it is shifted over another function.
And the given equation is solved with this given integral.
So, According to this theorem the equation becomes the
[tex]\mathscr{L} \left( \int_{0}^{t} e^{-\tau} \cos \tau d \tau \right) = \frac{ \mathscr{L} (e^{-\tau} \cos \tau ) }{s} \\\mathscr{L} \left( \int_{0}^{t} e^{-\tau} \cos \tau d \tau \right) = \frac{\frac{s+1}{(s+1)^2+1}}{s} \\\mathscr{L} \left( \int_{0}^{t} e^{-\tau} \cos \tau d \tau \right) = \frac{1}{s}\left (\frac{s+1}{(s+1)^2+1} \right).[/tex]
Then after solving, it become and with theorem it says that the
[tex]\mathscr{L} \left( \int_{0}^{t} f(\tau) d\tau \right) = \frac{\mathscr{L} ( f(\tau))}{s} .[/tex]
Hence by this way the given equation with convolution theorem is proved.
So, With convolution theorem the equation is proved.
Learn more about convolution theorem here
https://brainly.com/question/15409558
#SPJ4
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.
