System memory/Causality Question

[Schniz2]

Homework Statement

I need to state the Causality and whether it is a system with memory or a memory-less system and give reasons. The system is defined by:
(see 2.jpg below)... how do people type equations in message boards? :P

The Attempt at a Solution

Ok, so i have reasoned that the system is causal because if the input x(lambda) is zero, then the output will be the definite integral of zero which is equal to zero (i hope this is right). But then with the memory part I am having a bit of trouble... I am not sure i understand what the significance of the lambda variable is... is it an arbitrary point in time? because if so this would mean that it is a system with memory as the point in time could be less than t=0. Is it also assumed that lambda is only allowed to be less than or equal to t=0 because of the systems causality?
i hope this makes sense... i may be on the wrong track...

thanks

 

[LeBrad]

The system is causal if the output y(t) does not depend on future values of the input x(t). If t>0, then since the integral limits go from lambda= 0 to lambda = t, x(lambda) never depends on anything greater than t. However, if t<0, then y(t<0) depends on x(0), and is therefore not causal.

The system has memory if it depends on past or future values of the input or output. Since the integral sums up the input scaled by the time across all times between zero and t, the output clearly depends on past values of the input, so the system has memory.