(a) Find the Fourier sine and cosine transform of $f(x) = x^{n-1}$. (…

Previous year question for Numerical Methods & Transform Calculus.

Question

(a) Find the Fourier sine and cosine transform of $f(x) = x^{n-1}$.

(b) Find the Fourier sine integral for $f(x) = e^{-\beta x}$.

(c) Find the inverse Laplace transform of $\frac{s + 2}{(s^2 - 4s + 13)}$.

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