Find the laplace transform of the piece wise function

This isn't necessarily a matlab question but, I have to find the laplace transform of

f(t) { 0 when t <pi
       t-pi when pi<=t<2pi
       0 when t >= 2pi

Answer 1

[Walter Roberson]

http://www.mathworks.com/help/symbolic/laplace.html

[Sam]

Is there anyway you would be able to post a solution that shows how to find the answer by hand?

[Walter Roberson]

evalin(symengine, 'laplace(piecewise([t < Pi, 0], [Pi <= t, t-Pi], [t < 2*Pi, 0]),t,s)')

Answer 2

[Torsten]

L(s)=int_{t=pi}^{t=2*pi}(t-pi)*exp(-s*t) dt

For comparison:

http://www.wolframalpha.com/input/?i=intgeration&a=*C.intgeration-_*Calculator.dflt-&f2=(x-Pi)*Exp%5B-s*x%5D&f=Integral.integrand_(x-Pi)*Exp%5B-s*x%5D&f3=Pi&f=Integral.rangestart_Pi&f4=2*Pi&f=Integral.rangeend_2*Pi&a=*FVarOpt.1-_**-.***Integral.variable---.**Integral.rangestart-.*Integral.rangeend---

You should be able to evaluate this integral.

Best wishes

Torsten.

[Walter Roberson]

This does not appear to have taken into account the piecewise nature of the function ? The result I find using a different package is exp(-Pi*s)/s^2

[Torsten]

I get the same result when taking the Laplace transform directly:

http://www.wolframalpha.com/input/?i=Laplace+transform&a=*C.Laplace+transform-_*Calculator.dflt-&f2=Piecewise%5B%7B%7B0%2Ct%3CPi%7D%2C%7Bt-Pi%2Cpi%3C%3Dt%3C%3D2*Pi%7D%2C%7B0%2Ct%3E2*Pi%7D%7D%5D&f=LaplaceTransformCalculator.transformfunction_Piecewise%5B%7B%7B0%2Ct%3CPi%7D%2C%7Bt-Pi%2Cpi%3C%3Dt%3C%3D2*Pi%7D%2C%7B0%2Ct%3E2*Pi%7D%7D%5D&f3=t&f=LaplaceTransformCalculator.variable1%5Cu005ft&f4=s&f=LaplaceTransformCalculator.variable2%5Cu005fs

Best wishes

Torsten.