Success TrackerSuccess Tracker
Log inSign up

GATE EC 2015 Set 3 — Question 14

Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.
NAT+1 / -0MediumDefinite & Improper IntegralsCalculusEngineering MathematicsLaplace Transform & ROCLTI SystemsSignals & Systems

Engineering Mathematics → Calculus → Definite & Improper Integrals

Last updated

Question

Consider the function g(t)=e−tsin⁡(2πt)u(t)g(t) = e^{-t} \sin(2\pi t) u(t) where u(t)u(t) is the unit step function. The area under g(t)g(t) is ________.
Your answer

Enter a number. Decimals, negative values and scientific notation are accepted.

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 Calculus

2026 Set 1 Q11Consider the differential equation w⃗˙=Aw⃗\dot{\vec{w}} = A\vec{w}, with…2026 Set 1 Q12A surface is given by z2=2x2−y2z^2 = 2x^2 - y^2 and n⃗\vec{\mathbf{n}} and −n⃗-\vec{\mathbf{n}} are unit…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:…