%3D 312 110 However, this integral is zero for x 0 and These integral representations are call Laplace transform of sin(kx), while Bu is 2 LSECTION 42 PROBLEMS In each of Problems 1 through 10, find the Fourier cosine and sine integral representations of the func- tion. Determine what each integral representation converges to. x2 for 0 10 sin(x) for 0 27 1 for 0sx<1 3. f(x) ={2 for 1 4 cosh(x) for 0sx<5 4. (x) = for x> 5 14.3 The Fourier Transform We will use equation (14.4) to derive a con function, and then use this to define the For Suppose f is absolutely integrable on Then, at any x, 1 1 5((x+) + f(x-)) = Recall that cos(x)

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