GATE EE 2022 Set 1 — Question 41
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67EasyFundamental Theorem of CalculusCalculusEngineering MathematicsMaxima & Minima
Engineering Mathematics → Calculus → Fundamental Theorem of Calculus
Last updated
Question
Let . Then decreases in the interval
Correct answer
(A) x ∈ (1,2)
Solution
To find where decreases, we need to find the interval where its derivative is negative.
Using the Fundamental Theorem of Calculus (Leibniz Rule):
For to be decreasing, .
Since is always positive for all real , we must have:
This quadratic inequality holds when is between the roots 1 and 2.
Thus, , or .
Using the Fundamental Theorem of Calculus (Leibniz Rule):
For to be decreasing, .
Since is always positive for all real , we must have:
This quadratic inequality holds when is between the roots 1 and 2.
Thus, , or .
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 EE 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.
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 Q14Consider the following differential equation:…2026 Set 1 Q30Two matrices and have a common eigenvalue , and the same corresponding…2026 Set 1 Q32Given that , the integral…2026 Set 1 Q35 is an skew-symmetric matrix with real-valued entries, and is an…2026 Set 1 Q36A time-limited waveform is specified as follows:…