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Question: Heaviside integration question

Question:Heaviside integration question

nugtmaple 15 Maple
integration symbolic
August 08 2012
1

Does anyone know why the two integrations of a heaviside function (u1test and u2test) are not equal?  @Preben Alsholm said that the pure symbolic integration u was not correct so that the value of u2test is not correct either. Did I make any mistake in finding u? Is it possible for maple to find the pure symbolic expression of u correctly? Please help! @Markiyan Hirnyk


NULL

> 

restart

 

> 

assume(0 < ct, ct < cl, 0 < H, 0 < `&tau;l`, 0 < omega)
> 

NumericEventHandler(invalid_operation = `Heaviside/EventHandler`(value_at_zero = 1)):
> 

NULL
> 

u := simplify(int(int(Heaviside(t-ts-ys/ct), ys = H-cl*ts .. ct*ts), ts = H/(cl+ct) .. (H+cl*`&tau;l`)/(cl+ct))):
> 

u1test := simplify(int(int(Heaviside(t-ts-(1/3140)*ys), ys = H-6300*ts .. 3140*ts), ts = H/(6300+3140) .. (H+6300*`&tau;l`)/(6300+3140))):
> 

u2test := subs([cl = 6300, ct = 3140], u):
> 

combine(u1test-u2test)

(315/472)*t*Heaviside((1/9440)*H+(315/472)*`&tau;l`-(1/2)*t)*`&tau;l`+(1/9440)*t*Heaviside((1/9440)*H+(315/472)*`&tau;l`-(1/2)*t)*H+(197757/891136)*Heaviside((1/9440)*H+(315/472)*`&tau;l`-(1/2)*t)*H*`&tau;l`-(1/9440)*t*H*Heaviside((1/9440)*H-(1/2)*t)+(247275/118)*t*`&tau;l`*Heaviside(-(157/497700)*H+`&tau;l`+(37052/24885)*t)+(157/472)*H*t*Heaviside((1/6300)*H+`&tau;l`-(236/315)*t)+(247275/118)*t*`&tau;l`*Heaviside((1/6300)*H+`&tau;l`-(236/315)*t)-(24649/37288)*H*t*Heaviside(-(157/497700)*H+`&tau;l`+(37052/24885)*t)-(49455/111392)*H*`&tau;l`*Heaviside((1/6300)*H+`&tau;l`-(236/315)*t)-(49455/111392)*H*`&tau;l`*Heaviside(-(157/497700)*H+`&tau;l`+(37052/24885)*t)+(315/472)*t*`&tau;l`*Heaviside(t-(1/4720)*H+(24885/37052)*`&tau;l`)-(1492307/1482080)*H*t*Heaviside(t-(1/4720)*H+(24885/37052)*`&tau;l`)+(197757/891136)*H*`&tau;l`*Heaviside(t-(1/4720)*H+(24885/37052)*`&tau;l`)+(234235533/117084320)*H*t*Heaviside(t-(1/4720)*H)+(39193875/55696)*`&tau;l`^2*Heaviside(-(157/497700)*H+`&tau;l`+(37052/24885)*t)+(24649/351998720)*H^2*Heaviside(-(157/497700)*H+`&tau;l`+(37052/24885)*t)+(123245/79)*t^2*Heaviside(-(157/497700)*H+`&tau;l`+(37052/24885)*t)-785*t^2*Heaviside((1/6300)*H+`&tau;l`-(236/315)*t)-(157/4455680)*H^2*Heaviside((1/6300)*H+`&tau;l`-(236/315)*t)-(77891625/55696)*`&tau;l`^2*Heaviside((1/6300)*H+`&tau;l`-(236/315)*t)+785*t^2-(625216725/445568)*`&tau;l`^2*Heaviside(t-(1/4720)*H+(24885/37052)*`&tau;l`)+(62947647/878624450560)*H^2*Heaviside(t-(1/4720)*H+(24885/37052)*`&tau;l`)+(6303/2)*t^2*Heaviside(t-(1/4720)*H+(24885/37052)*`&tau;l`)-(12279222097/69411331594240)*H^2*Heaviside(t-(1/4720)*H)-(868457/158)*t^2*Heaviside(t-(1/4720)*H)-(3139/178227200)*Heaviside((1/9440)*H-(1/2)*t)*H^2+(3143/8)*Heaviside((1/9440)*H-(1/2)*t)*t^2-(989415/472)*t*`&tau;l`+(3139/178227200)*Heaviside((1/9440)*H+(315/472)*`&tau;l`-(1/2)*t)*H^2+(311467275/445568)*Heaviside((1/9440)*H+(315/472)*`&tau;l`-(1/2)*t)*`&tau;l`^2-(157/472)*H*t+(197883/891136)*H*`&tau;l`-(3143/8)*Heaviside((1/9440)*H+(315/472)*`&tau;l`-(1/2)*t)*t^2+(311665725/445568)*`&tau;l`^2+(157/4455680)*H^2

 (1)
> 

uplot1 := subs([H = .183, `&tau;l` = 0.492e-6, `&tau;t` = 0.2e-5, omega = 2*Pi*0.715e7], u1test):
> 

uplot2 := subs([H = .183, `&tau;l` = 0.492e-6, `&tau;t` = 0.2e-5, omega = 2*Pi*0.715e7], u2test):
> 

plot(uplot1, t = 0.37e-4 .. 0.41e-4)

 
> 

plot(uplot2, t = 0.37e-4 .. 0.41e-4)

 

``


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