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(Solved): 5.25. (a) Find the Fourier transform of f(x)={(1-x^(2),|x|<1),(0,|x|>1):}. (b) Evaluate \int_0 ...
5.25. (a) Find the Fourier transform of f(x)={(1-x^(2),|x|<1),(0,|x|>1):}.
(b) Evaluate \int_0^(\infty ) ((xcosx-sinx)/(x^(3)))cos((x)/(2)dx).
5.26. If f(x)={(1,0<=x<1),(0,x>=1):} find (a) the Fourier sine transform, (b) the Fourier cosine trans-
form of f(x). In each case obtain the graphs of f(x) and its transform.