Question: Use the Parseval relation to evaluate (a) J -00 (b) / do (w + a) w dw (w + a) (a) Show that the

Use the Parseval relation to evaluate (a) J -00 (b) / do

(w + a) w dw (w + a) (a) Show that the

Fourier sine and cosine transforms of e-atare 2 2 a = 6

Use the Parseval relation to evaluate (a) J -00 (b) / do (w + a) w dw (w + a) (a) Show that the Fourier sine and cosine transforms of e-atare 2 2 a = 6 + = ta Tw + a 8c (w): Hint. Each of the transforms can be related to the other by integration by parts. 8s (w) = (b) Show that @sin wx w + a 0 -do cos cx w + a 1=1/e-ax dw= - e-ar 2a x > 0, x > 0.

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