(a) If f(t) = t m and g(t) = t n, where m and n are posi
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(a) If f(t) = t m and g(t) = t n, where m and n are positive integers, show that (f ? g)(t) = t m+n+1 ? 1 0 um(1 ? u) n
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(a) If f(t) = t m and g(t) = t n, where m and n are positive integers, show that (f ? g)(t) = t m+n+1 ? 1 0 um(1 ? u) n du. (b) Use the convolution theorem to show that ? 1 0 um(1 ? u) n du = m! n! (m + n + 1)! . (c) Extend the result of part (b) to the case where m and n are positive numbers but not necessarily integers. In each of Problems 14 through 21, express the total response of the given initial value problem using a convolution integral to represent the forced response:
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