# Consider the integrator and check for time invariance

I'm trying to check the following system for for time-invariance.

$$y(t) = \int_0^t x(\lambda) d\lambda$$

Please explain me why it is time-invariant.

• Could you explain why you think it is time-invariant? – Matt L. Apr 14 at 10:47
• I think it's a time-variant... but Is it time invariant? – heldi Apr 14 at 11:29
• You should show your calculations and your conclusions. We can't do your homework for you, but we can help you doing it. – Matt L. Apr 14 at 11:51
• You better add that to your question. – Matt L. Apr 14 at 11:58
• Check how I added the equation to your question (using Latex formatting), and use that to add the steps that you came up with. – Matt L. Apr 14 at 12:01

$$y(t)=\int_{-\infty}^tx(\tau)d\tau\tag{1}$$
$$y(t)=\int_{t-T}^tx(\tau)d\tau\tag{2}$$