Consider a continuous-time signal $x(t) = -t^2 u(t + 4) - u(t - 4)$ where $u(t)$ is the continuous-time unit step function. Let $\delta(t)$ be the continuous-time unit impulse function. The value of $$\int{-\infty}^{\infty} x(t)\delta(t + 3)dt$$ is

Let continuous-time signals $x1(t)$ and $x2(t)$ be $x1(t) = \begin{cases} 1, & t \in 0,1 \\ 2-t, & t \in 1,2 \\ 0, & \text{otherwise} \end{cases} \quad \text{and} \quad x2(t) = \begin{cases} t, & t \in 0,1 \\ 2-t, & t \in 1,2 \\ 0, & \text{otherwise} \end{cases}$ Consider the convolution $y(t) = x1(t) x2(t)$. Then $\int{-\infty}^{\infty} y(t)dt$ is

Consider a discrete-time linear time-invariant (LTI) system $S$, where $$yn = S\{xn\}$$ Let $$S\{\deltan\} = \begin{cases} 1, & n \in \{0, 1, 2\} \\ 0, & \text{otherwise} \end{cases}$$ where $\deltan$ is the discrete-time unit impulse function. For an input signal $xn$, the output $yn$ is