JEE Main 2021 — Definite Integration Question with Solution
From: JEE Main 2021 (Online) 24th February Evening Shift
Question
Let f(x) be a differentiable function defined on [0, 2] such that f'(x) = f'(2 x) for all x (0, 2), f(0) = 1 and f(2) = e2. Then the value of is :
Choose an option
Show full solutionCorrect option: A
Correct answer
A1 + e2
Step-by-step explanation
f'(x) = f'(2 x)
On integrating both side f(x) = f(2 x) + c
put x = 0
f(0) + f(2) = c c = 1 + e2
f(x) + f(2 x) = 1 + e2 ..... (i)
On integrating both side f(x) = f(2 x) + c
put x = 0
f(0) + f(2) = c c = 1 + e2
f(x) + f(2 x) = 1 + e2 ..... (i)
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This is a previous-year question from JEE Main 2021, 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.