JEE Advanced 2023 | Differential Equation PYQ | Maths | Full Concepts Explain

Описание: Let f:[1,∞)→R be a differentiable function such that f(1)=1/3 and 3∫_1^x▒〖f(t)dt =xf(x)-x^3/3,〗
xϵ[1,∞).Let e denote the base of the natural logarithm.Then the value of f(e) is
(A)(e^2+4)/3 (B) log_e⁡〖4+e〗/3
(C) (4e^2)/3 (D) (e^(2 )-4)/3
JEE Advanced 2023
This question is a classic JEE Advanced pattern where an integral equation is converted into a differential equation — a concept that keeps repeating in JEE.
If you understand this properly, you can solve many future questions in seconds.
🔥 Why this video is important
• Repeating concept in JEE Advanced
• Integral → Differential Equation trick
• Short method explained
• Helps in rank-boost questions
• Strong concept for 2025–2026 aspirants

If you are preparing seriously for JEE (Mains+Advanced,) do not skip this type of question.

🎯 What you’ll learn

✔ Leibniz rule application
✔ Converting integral relation into DE
✔ Fast solving approach
✔ Exam-oriented thinking

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📌 For serious JEE students

Watch till the end and try to solve before seeing the solution.
This exact concept has appeared multiple times in JEE Advanced.

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🔔 Support

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More videos coming on:
Differential Equation
Definite Integration
Limits
AOD