JEE Main 2015MathematicsDefinite IntegrationHardMCQ

JEE Main 2015 — Definite Integration Question with Solution

JEE Main 2015 (11 Apr Online)

Question

Let f:R→R be a function such that f2-x=f2+x and f4-x=f4+x, for all x∈R and ∫02fxdx=5. Then the value of ∫1050fxdx is

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Show full solutionCorrect option: A
Correct answer
A100

Step-by-step explanation

f2-x=f2+x and f4-x=f(4+x)

Then curve is symmetric about x=2 and x=4

∴    The curve is periodic with period 4

Given ∫02fxdx=5

∫04fxdx=2∫02fxdx=10

∫1050fxdx=∫24+2124+2fxdx

=12-2∫04fxdx

=10×10=100

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About this question

This is a previous-year question from JEE Main 2015, 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.