Find the Fourier transform of f(x) given that f(x) = sgn(x)e™ax|, where a > 0 and sgn(x) is the signum (or sign) function that is defined as follows (-1 for x<0, sgn(x) = } 0 for x = 0, 1 for x> 0. Hence, using the Parseval's relation, evaluate the integral w? I = - (a? dw. + w?)²

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