This problem requires you to plot Fourier integral approximations to
a function. Almost certainly you will need to use Maple to do this
problem

We want a plot of f(x), together with approximations for M=1, 5, 25
for the range -10 < x < 10.



> f:=piecewise(x<-5,0,x<0,-1,x<5,1,0);
                               { 0          x < -5
                               {
                               { -1          x < 0
                          f := {
                               { 1           x < 5
                               {
                               { 0         otherwise


This is maple for the function
	f(x) = -1 from -5 < x < 0
	f(x) =  1 from  0 < x < 5
	f(x) is zero otherwise.

> Bw:=(2/Pi)*int(f*sin(w*x),x=0..5);       
                                   2 (-1 + cos(5 w))
                           Bw := - -----------------
                                         Pi w

> # Fourier Integral f(x) = Int(Bw * sin (w*x),w=0..infinity);
                        infinity
                       /
                      |            2 (-1 + cos(5 w)) sin(w x)
              f(x) =  |          - -------------------------- dw
                      |                       Pi w
                     /
                       0

> gM:=int(Bw * sin (w*x),w=0..M);              
                   -2 Si(M x) + Si((x + 5) M) + Si((x - 5) M)
                 - ------------------------------------------
                                       Pi

> g1 := eval(gM,M=1);
> g5 := eval(gM,M=5);
> g25 := eval(gM,M=25);

> plot([f,g1,g5,g25],x=-10..10,color=[black,black,blue,red]);