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Question: MENTAL BLOCK: Integration conflict

Question:MENTAL BLOCK: Integration conflict

tsunamiBTP 292 Maple 12
integral
May 10 2018
0

This should be a simple problem, but I am having trouble resolving a contradiction in integral evaluation that is included in the results below.  Instead of butting my head further perhaps someone can point out my probable error.

You will see in both cases I have a triangle signal with a slope of (-1).  However in the 2nd case I have linked the period T to the slope parameter alpha.  If I assign alpha=1 then the results of the 2 integrals should = 1/4, but the 2nd one does not.

Appreciate any feedback.


 

plot(piecewise(-1 < x and x < 0, 0, 0 < x and x < 1, 1-x), x = -2 .. 2, linestyle = solid, thickness = 5, scaling = constrained, title = "Asymmetric Triangle Wave", titlefont = [COURIER, 18])

  

n := 0; 1; T := 2; 1; a[0] := (int(0*exp(-I*(2*Pi*n*t/T)), t = -(1/2)*T .. 0)+int((1-t)*exp(-I*(2*Pi*n*t/T)), t = 0 .. (1/2)*T))/T

1/4

 (1)

restart

alpha := 1; T := 2/alpha; plot(piecewise(x < 0, 0, 0 < x and x < (1/2)*T, -alpha*x+1), x = -T .. T, linestyle = solid, thickness = 5, scaling = constrained, title = "Asymmetric Triangle Wave", titlefont = [COURIER, 18])

  

  n=0 term:n := 0; 1; alpha := 1; 1; T := 2; 1; a[0] := (int(0*exp(-I*(2*Pi*n*t/T)), t = -(1/2)*T .. 0)+int((1-alpha*T)*exp(-I*(2*Pi*n*t/T)), t = 0 .. (1/2)*T))/T

-1/2

 (2)

``


 

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