JEE Main 2024 — Definite Integration Question with Solution
From: JEE Main 2024 (Online) 31st January Morning Shift
Question
Let be a function defined by and M=\int_\limits{f(a)}^{f(1-a)} x \sin ^4(x(1-x)) d x, N=\int_\limits{f(a)}^{f(1-a)} \sin ^4(x(1-x)) d x ; a \neq \frac{1}{2}. If , then the least value of is equal to __________.
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Show full solutionCorrect answer: 1
Step-by-step explanation
M=\int_\limits{f(a)}^{f(1-a)}(1-x) \cdot \sin ^4 x(1-x) d x
Ans. 5
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This is a previous-year question from JEE Main 2024, covering the Definite Integration chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.