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Error estimates of approximations in real domain for the Fourier transform and in complex domain for the Laplace and Mellin transform are presented for functions f which vanish beyond a finite domain [a,b]⊂[0,∞> and whose derivative belongs to L_{p}[a,b]. New inequalities involving integral transform of f, integral mean of f and exponential and logarithmic mean of the endpoints of the domain of f are given. These estimates enables us to obtain associated numerical quadrature rules for each transform and error bounds of their remainders.