(a) Show that (10) implies

(b) Solve Prob. 8 by applying (a3) to the result of Prob. 7.

Data from Prob. 7

Represent f(x) as an integral (10).

(c) Verify (a2) for f(x) = 1 if 0 < x < α and f(x) = 0 if x > α.
(d) Find formulas for the Fourier sine integral similar to those in (a).

f(ax) = | a() cos. (al) cos xw dw (Scale change) (a > 0) B* (w) sin xw dw, (a2) xf(x) dA A as in (10) B* = dw x*f(x) = | A*(w) cos xw dw, (a3) d?A A* = dw2 if 0