The GATE Grind

GATE 2025 EE – Question 21

Signals and Systems · Representation of continuous and discrete time signals, shifting and scaling properties · 1 mark · Multiple choice

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

  1. −9
  2. 9
  3. 3
  4. −3

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) −9

Explanation

By the sifting property, the integral equals $x(-3)$. Since $-3$ lies inside $(-4,4)$, $u(t+4)-u(t-4)=1$ there, so $x(-3)=-(-3)^2=-9$.