Question

Is the integral of sin(t) from -infinity to +t defined? Upon integration you would find that -cos(-infinity) does not exist. Is the integral of sin(t) from +t to +infinity defined? If similarly no, then if taking the sum of the two integrals, would the integral of sin(t) from -infinity to +infinity be undefined?

Answer 1

Do none of that. \(\sin(t)\) does nothing cooperative as t increases without bound. It just continues to oscillate. Such an integral does not converge.

Please never write that thing with cosine and infinity again. That is quite meaningless and confusing.

Answer 2

A signal u(t) such as a sine function u(t) = sin(t) can be a signal to the following systems model of a control system. How would the model respond?

Answer 3

1) Such a mode doesn't seem to exist, since there is no convergence on the "R" side.
2) If you wuld like to cut it off at something finite, then we can get an oscillating system.

Answer 4

So an input signal u(t) = sin(t) would work in this equation and something finite will come out. Thank you.

Answer 5

You have to switch it on. It cannot have been running forever.

Answer 6

Mmm, right. Thanks.