Question

A voltage of 10 V is switched on at t=4sec.This voltage is applied to the input of an integrator.What is the output voltage.
Options are;
1)10t u(t-4)
2)4t u(t)
3)10(t-4) u(t-4)
4)10t^2 u(t+4)

Answer 1

I would say the answer is 1.

Answer 2

The antiderivative of 10 is 10t, and since the switch was off up to 4 sec, we multiply it by u(t-4). u(t-4) makes 10t equal zero up to the point t=4sec, and then it's equal to 10t from t=4 to infinity.