Success TrackerSuccess Tracker
Log inSign up

GATE EC 2014 Set 1 — Question 37

Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.
MCQ+2 / -0.67HardFourier Transform & PropertiesContinuous-Time SignalsSignals & Systems

Signals & Systems → Continuous-Time Signals → Fourier Transform & Properties

Last updated

Question

For a function g(t)g(t), it is given that ∫−∞+∞g(t)e−jωtdt=ωe−2ω2\int_{-\infty}^{+\infty} g(t)e^{-j\omega t} dt = \omega e^{-2\omega^2} for any real value ω\omega. If y(t)=∫−∞tg(τ)dτy(t) = \int_{-\infty}^{t} g(\tau) d\tau, then ∫−∞+∞y(t)dt\int_{-\infty}^{+\infty} y(t)dt is
Your answer

Choose one option, then check your answer.

The solution stays hidden until you check.

Continue learning with Success Tracker

A step still unclear? Work through it with support

Use Success Tracker to ask about the reasoning, then try another GATE EC question to check your understanding.

AI-powered practice· Unlimited practice on eligible plans
PYQs with solutions
Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
Practice that adapts
Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
AI doubt support
Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.

Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.

Start with a free accountView plans and allowances

This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.

More questions on Continuous-Time Signals

2026 Set 1 Q13The Laplace Transform of the signal x(t)=u(t−2)∗(tu(t))x(t) = u(t - 2) * (tu(t)) is given by which of the following…2026 Set 1 Q15Two analog signals x1(t)x_1(t) and x2(t)x_2(t) (tt in second), are sampled at a rate Fs=40F_s = 40 Hz,…2026 Set 1 Q16The response of a discrete time system y[n]y[n] obeys the following relation:…2026 Set 1 Q37The continuous time signal x(t)x(t) is real, periodic with period TT and satisfies the Dirichlet…2026 Set 1 Q43Consider a real signal x(t)x(t), −∞<t<∞-\infty < t < \infty, such that x(t)=0x(t) = 0 for t<0t < 0, x(t)=2x(t) = 2…