Need help with simple unit step functions, (for Laplace transforms)?

Hi, here's my question...

I am required to find the Laplace transform of the given function which is assumed to be zero outside the interval.

t^2 (0<t<1)

I have to first rewrite it in terms of unit step functions, and that's the step i dont understand?

The solution manual writes it as (t^2)[1-u(t-1)] where u denotes unit step function....

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what's confusing for me is that for t<0, say t=-2, the value of the function (provided by solution manual) will be 4. where originally the function was "assumed to be zero" outside the interval......and -2 is outside the interval...

please explain..

Re: Need help with simple unit step functions, (for Laplace transforms)?

Are you required to use unit step function? A straight forward integration by parts will provide you the Laplace transform of the function t^2 (0<t<1).