With details please everything V.Find the exponential Fourier transform g(a) of the given function f(x) andwrite it as a Fourier integral (find g(a) in equation (12.2) and substitute yourresult into the first integral in equation (12.2)).[1, 0 UMM AL-QURA UNIVERSITYCollege of Applied ScienceDepartment of PhysicsI.II.III.IV.b.f(x) =(9.4)Calculate the average values of the following functions on the given intervals:. f(x) = sin x on the interval (0,7)• g(x) = 1-e* on the interval (0,1)-xIn each of the following problems you are given a function on the interval - <x < 7. Sketch several periods of the corresponding periodic function of period27. Expand the periodic function in a sine-cosine Fourier series:a.(9.5)f(x)=1,HAHA1,0, -T

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In each of the following problems you are given a function on the interval - < x < . Sketch several periods of the corresponding periodic function of period 27. Expand the periodic function in a sine-cosine Fourier series: a. b. f(x) = -1, -<*1, x <n. 0, f(x) = 1, π Sketch each of the following functions on the interval (-1,1) and expand it in a sine-cosine series. f(x) = -{t 1, -<x<0, ㅠ 0<x< 2' <<n. -{ f(x)= 0 < x < 1. The functions f is given over one period. Sketch several periods and decide whether it is even or odd, then use (9.4) or (9.5) to expand it in an appropriate Fourier series. -1 < x < 0, -1, -< < 0, 0<x<n.