transgalactic
Banned
i need to prove that
[latex]
M_{f(t)}=0.5\int_{t-1}^{t+1}f(u)du
[/latex]
is time invarient
?
i know that
i need to get the same result for a shift in time
[latex]
M_{f(t-x)}=0.5\int_{t-1-x}^{t-x+1}f(u-x)du
[/latex]
u-x=s -> du=ds
[latex]
M_{f(t-x)}=0.5\int_{t-1-x}^{t-x+1}f(s)ds
[/latex]
so what now??
how does it prove that
[latex]
M_{f(t-x)}=M_{f(t)}
[/latex]
??
??
[latex]
M_{f(t)}=0.5\int_{t-1}^{t+1}f(u)du
[/latex]
is time invarient
?
i know that
i need to get the same result for a shift in time
[latex]
M_{f(t-x)}=0.5\int_{t-1-x}^{t-x+1}f(u-x)du
[/latex]
u-x=s -> du=ds
[latex]
M_{f(t-x)}=0.5\int_{t-1-x}^{t-x+1}f(s)ds
[/latex]
so what now??
how does it prove that
[latex]
M_{f(t-x)}=M_{f(t)}
[/latex]
??
??
Last edited: